Graham was born in Glasgow, Scotland. Graham's father was a successful textile manufacturer, and wanted his son to enter into the Church of Scotland. Instead, defying his father's wishes, Graham became a student at the University of Glasgow in 1819. There he developed a strong interest in chemistry, and left the University after receiving his M.A. in 1826. He later became a professor of chemistry at numerous colleges, including the Royal College of Science and Technology and the University of London.

Graham also founded the Chemical Society of London in 1841. In 1866, he was elected a foreign member of the Royal Swedish Academy of Sciences.

His final position was as the Master of the Mint, where he stayed for 15 years until his death. He was the last person to hold that position.

Thomas Graham is best known for two things:

1. His studies on the diffusion of gases resulted in "Graham's Law", which states that the rate of effusion of a gas is inversely proportional to the square root of its molar mass.
2. His discovery of dialysis, which is used in many medical facilities today, was the result of Graham's study of colloids. This work resulted in Graham's ability to separate colloids and crystalloids using a so-called "dialyzer", the precursor of today's dialysis machine. This study initiated the scientific field known as colloid chemistry, of which Graham is credited as the founder.