While in the U.S., in the midst of the war, his friend John von Neumann invited him to a secret project in New Mexico. Ulam researched the invitation by checking out a book on New Mexico from the university library. He found on the book's check-out card the names of all those who had successively disappeared from the campus at the UW. Ulam then joined the Manhattan Project at Los Alamos.

While there, he suggested the Monte Carlo method for evaluating complicated mathematical integrals that arise in the theory of nuclear chain reactions (not knowing that Fermi and others had used a similar method earlier). This suggestion led to the more systematic development of Monte Carlo by Von Neumann, Metropolis, and others.

Ulam—in collaboration with C.J. Everett, who did the detailed calculations—showed Edward Teller's early model of the hydrogen bomb to be inadequate. Ulam then went on to suggest a better method. He was the first to realize that one could place all the H-bomb's components inside one casing, put a fission bomb at one end and thermonuclear material at the other, and use mechanical shock from the fission bomb to compress and detonate fusion fuel. This idea was probably an outcome of Ulam's initial ideas for 'staging' a conventional fission device, in which the neutron flux from one fission bomb would compress the fuel in another one, thus increasing its efficiency. Teller at first resisted this idea, then saw its merit and suggested the use of a plutonium "spark plug", located at the center of the fusion fuel, to initiate and enhance the fusion reaction. Teller also modified Ulam's idea of compression by realizing that radiation from the fission bomb would compress the thermonuclear fuel much more efficiently than mechanical shock. This design, called staged radiation implosion, has since been the standard method of creating H-bombs. Although this approach was long believed to have been worked out independently by Soviet physicist Andrei Sakharov, it is often referred to as the "Teller–Ulam design". Ulam and Teller jointly applied for a patent on the hydrogen bomb.

Ulam also invented nuclear pulse propulsion and, at the end of his life, declared it the invention of which he was proudest.

He was an early proponent of using computers to perform "mathematical experiments." His most notable contribution here may have been his part in the Fermi–Pasta–Ulam experiments, an early numerical study of a dynamical system. Another dynamical system he introduced is the well-known Fermi–Ulam model (FUM), that is a variant of Fermi's primary work on acceleration of cosmic rays, namely Fermi acceleration. FUM became over the years a prototype model for studying non-linear dynamics and coupled mappings.

In pure mathematics, he worked in set theory (including measurable cardinals and abstract measures), topology, ergodic theory, and other fields. After World War II he largely turned from rigorous pure mathematics to speculative work, posing problems and making conjectures often concerning the application of mathematics to physics and biology. His friend Gian-Carlo Rota ascribed this change to an attack of encephalitis in 1946 that Rota claimed changed Ulam's personality (though detail had never been Ulam's strong point). This suggestion is believed by many but rejected by Ulam's widow, Françoise, among others.

Ulam took a position at the University of Colorado in 1965. As he remained a consultant at Los Alamos, he divided his time between Boulder, Colorado, and Santa Fe, New Mexico, from which he commuted to Los Alamos. Later he and his wife spent winters in Gainesville, Florida, where he had a position with the University of Florida. He died in Santa Fe on May 13, 1984.