Bohm was born in Wilkes-Barre, Pennsylvania to a Hungarian Jewish immigrant father and a Lithuanian Jewish mother. He was raised mainly by his father, a furniture store owner and assistant of the local rabbi. Bohm attended Pennsylvania State College (now The Pennsylvania State University), graduating in 1939, then attended the California Institute of Technology for a year, and then transferred to the theoretical physics group directed by Robert Oppenheimer at the University of California, Berkeley, where he eventually obtained his doctorate degree.

Bohm lived in the same neighborhood as some of Oppenheimer's other graduate students (Giovanni Rossi Lomanitz, Joseph Weinberg, and Max Friedman) and with them became increasingly involved not only with physics, but with radical politics. Bohm became active in organizations like the Young Communist League, the Campus Committee to Fight Conscription, and the Committee for Peace Mobilization all later termed Communist organizations by J. Edgar Hoover's FBI.

During World War II, the Manhattan Project mobilized much of Berkeley's physics research in the effort to produce the first atomic bomb. Though Oppenheimer had asked Bohm to work with him at Los Alamos (the top secret laboratory established in 1942 to design the atom bomb), the director of the Manhattan Project, General Leslie Groves, would not approve Bohm's security clearance, after evidence about his politics (Bohm's friend, Joseph Weinberg, had also been suspected for espionage).

Bohm remained in Berkeley, teaching physics, until he completed his Ph.D. in 1943, by an unusually ironic circumstance. According to Peat, "the scattering calculations (of collisions of protons and deuterons) that he had completed proved useful to the Manhattan Project and were immediately classified. Without security clearance, Bohm was denied access to his own work; not only would he be barred from defending his thesis, he was not even allowed to write his own thesis in the first place!" To satisfy the university, Oppenheimer certified that Bohm had successfully completed the research. He later performed theoretical calculations for the Calutrons at the Y-12 facility in Oak Ridge, used to electromagnetically enrich uranium for use in the bomb dropped on Hiroshima in 1945.

After the war, Bohm became an assistant professor at Princeton University, where he worked closely with Albert Einstein. In May, 1949, at the beginning of the McCarthyism period, the House Un-American Activities Committee called upon Bohm to testify before it — because of his previous ties to suspected Communists. Bohm, however, pleaded the Fifth amendment right to refuse to testify, and refused to give evidence against his colleagues.

In 1950, Bohm was charged for refusing to answer questions of the Committee and was arrested. He was acquitted in May, 1951, but Princeton University had already suspended him. After the acquittal, Bohm's colleagues sought to have him re-instated to Princeton, and Einstein reportedly wanted Bohm to serve as his assistant. The university, however, did not renew his contract. Bohm then left for Brazil to assume a professorship of Physics at the University of São Paulo.

During his early period, Bohm made a number of significant contributions to physics, particularly to quantum mechanics and relativity theory. As a post - graduate at Berkeley, he developed a theory of plasmas, discovering the electron phenomenon known now as Bohm diffusion. His first book, Quantum Theory published in 1951, was well received by Einstein, among others. However, Bohm became dissatisfied with the orthodox interpretation of quantum theory, which he had written about in that book, and began to develop his own interpretation (De Broglie – Bohm theory) — a non-local hidden variable deterministic theory the predictions of which agree perfectly with the nondeterministic quantum theory. His work and the EPR argument became the major factor motivating John Bell's inequality, the consequences of which are still being investigated.

In 1955, Bohm relocated to Israel, where he spent two years working at the Technion at Haifa. Here he met Sarah Woolfson (also called Saral). The couple married in 1956. In 1957, Bohm relocated to the United Kingdom as a research fellow at the University of Bristol. In 1959, Bohm and his student Yakir Aharonov discovered the Aharonov - Bohm effect, showing how a magnetic field could affect a region of space in which the field had been shielded, although its vector potential did not vanish there. This showed for the first time that the magnetic vector potential, hitherto a mathematical convenience, could have real physical (quantum) effects. In 1961, Bohm was made Professor of Theoretical Physics at the University of London's Birkbeck College, where his collected papers are kept.

In collaboration with Stanford neuroscientist Karl Pribram Bohm was involved in the early development of the holonomic model of the functioning of the brain, a model for human cognition that is drastically different from conventionally accepted ideas. Bohm worked with Pribram on the theory that the brain operates in a manner similar to a hologram, in accordance with quantum mathematical principles and the characteristics of wave patterns.

Bohm was alarmed by what he considered an increasing imbalance of not only man and nature, but among peoples, as well as people, themselves. Bohm: "So one begins to wonder what is going to happen to the human race. Technology keeps on advancing with greater and greater power, either for good or for destruction." He goes on to ask:

What is the source of all this trouble? I'm saying that the source is basically in thought. Many people would think that such a statement is crazy, because thought is the one thing we have with which to solve our problems. That's part of our tradition. Yet it looks as if the thing we use to solve our problems with is the source of our problems. It's like going to the doctor and having him make you ill. In fact, in 20% of medical cases we do apparently have that going on. But in the case of thought, it's far over 20%.

In Bohm's view:

...the general tacit assumption in thought is that it's just telling you the way things are and that it's not doing anything - that 'you' are inside there, deciding what to do with the info. But you don't decide what to do with the info. Thought runs you. Thought, however, gives false info that you are running it, that you are the one who controls thought. Whereas actually thought is the one which controls each one of us. Thought is creating divisions out of itself and then saying that they are there naturally. This is another major feature of thought: Thought doesn't know it is doing something and then it struggles against what it is doing. It doesn't want to know that it is doing it. And thought struggles against the results, trying to avoid those unpleasant results while keeping on with that way of thinking. That is what I call "sustained incoherence".

Bohm thus proposes in his book, Thought as a System, a pervasive, systematic nature of thought:

What I mean by "thought" is the whole thing - thought, felt, the body, the whole society sharing thoughts - it's all one process. It is essential for me not to break that up, because it's all one process; somebody else's thoughts becomes my thoughts, and vice versa. Therefore it would be wrong and misleading to break it up into my thoughts, your thoughts, my feelings, these feelings, those feelings... I would say that thought makes what is often called in modern language a system. A system means a set of connected things or parts. But the way people commonly use the word nowadays it means something all of whose parts are mutually interdependent - not only for their mutual action, but for their meaning and for their existence. A corporation is organized as a system - it has this department, that department, that department. They don't have any meaning separately; they only can function together. And also the body is a system. Society is a system in some sense. And so on. Similarly, thought is a system. That system not only includes thoughts, "felts" and feelings, but it includes the state of the body; it includes the whole of society - as thought is passing back and forth between people in a process by which thought evolved from ancient times. A system is constantly engaged in a process of development, change, evolution and structure changes... although there are certain features of the system which become relatively fixed. We call this the structure.... Thought has been constantly evolving and we can't say when that structure began. But with the growth of civilization it has developed a great deal. It was probably very simple thought before civilization, and now it has become very complex and ramified and has much more incoherence than before. Now, I say that this system has a fault in it - a "systematic fault". It is not a fault here, there or here, but it is a fault that is all throughout the system. Can you picture that? It is everywhere and nowhere. You may say "I see a problem here, so I will bring my thoughts to bear on this problem". But "my" thought is part of the system. It has the same fault as the fault I'm trying to look at, or a similar fault. Thought is constantly creating problems that way and then trying to solve them. But as it tries to solve them it makes it worse because it doesn’t notice that it's creating them, and the more it thinks, the more problems it creates.

To address societal problems during his later years, Bohm wrote a proposal for a solution that has become known as " Bohm Dialogue", in which equal status and "free space" form the most important prerequisites of communication and the appreciation of differing personal beliefs. He suggested that if these Dialogue groups were experienced on a sufficiently wide scale, they could help overcome the isolation and fragmentation Bohm observed was inherent in society.

Bohm continued his work in quantum physics past his retirement in 1987. His final work, the posthumously published The Undivided Universe: An ontological interpretation of quantum theory (1993), resulted from a decades long collaboration with his colleague Basil Hiley. He also spoke to audiences across Europe and North America on the importance of dialogue as a form of sociotherapy, a concept he borrowed from London psychiatrist and practitioner of Group Analysis Patrick De Mare, and had a series of meetings with the Dalai Lama. He was elected Fellow of the Royal Society in 1990.

Near the end of his life, Bohm began to experience a recurrence of depression which he had suffered at earlier times in his life. He was admitted to the Maudsley Hospital in South London on 10 May 1991. His condition worsened and it was decided that the only treatment that might help him was electroconvulsive therapy. Bohm's wife consulted psychiatrist David Shainberg, Bohm's long time friend and collaborator, who agreed that electroconvulsive treatments were probably his only option. Bohm showed improvement from the treatments and was released on 29 August. However, his depression returned and was treated with medication.

David Bohm died of a heart failure in Hendon, London, on 27 October 1992, aged 74. He had been traveling in a London taxicab on that day; after not getting any response from the passenger in the back seat for a few seconds, the driver turned back and found that Dr. Bohm had died. David Bohm was widely considered one of the best quantum physicists of all time.