Tamm's father was an engineer in the city of Yelizavetgrad (now Kirovohrad, Ukr.), where he was responsible for building and managing electric power stations and water systems. Tamm graduated from the gymnasium there in 1913 and went abroad to study at the University of Edinburgh. The following year he returned to Moscow State University, and he graduated in 1918. In 1924 he became a lecturer in the physics department, and in 1930 he succeeded his mentor, Leonid I. Mandelstam, to the chair of theoretical physics. In 1933 Tamm was elected a corresponding member of the Soviet Academy of Sciences (Sciences, Academy of). The following year, he joined the P.N. Lebedev Physics Institute of the Soviet Academy of Sciences (FIAN), where he organized and headed the theoretical division, a position he occupied until his death.

Tamm's early studies of unique forms of electron bonding (“Tamm surface levels”) on the surfaces of crystalline solids had important applications in the later development of solid-state semiconductor devices (semiconductor device). In 1934 Cherenkov had discovered that light is emitted when gamma rays (gamma ray) pass through a liquid medium. In 1937 Tamm and Frank explained this phenomenon as the emission of light waves by electrically charged particles moving faster than the speed of light in a medium. Tamm developed this theory more fully in a paper published in 1939. For these discoveries Tamm, Frank, and Cherenkov received the 1958 Nobel Prize for Physics.

Immediately after World War II, Tamm, though a major theoretician, was not assigned to work on the atomic bomb project, possibly for political reasons. In particular, he was branded a “bourgeois idealist” and his brother an “enemy of the state.” Nevertheless, in June 1948, when physicist Igor V. Kurchatov (Kurchatov, Igor Vasilyevich) needed a strong team to investigate the feasibility of creating a thermonuclear bomb, Tamm was recruited to organize the theoretical division of FIAN in Moscow. The Tamm group came to include physicists Yakov B. Zeldovich, Vitaly L. Ginzburg (Ginzburg, Vitaly Lazarevich), Semyon Z. Belenky, Andrey D. Sakharov (Sakharov, Andrey Dmitriyevich), Efim S. Fradkin, Yuri A. Romanov, and Vladimir Y. Fainberg. Between March and April 1950, Tamm and several members of his group were sent to the secret installation known as Arzamas-16 (near the present-day village of Sarov) to work under physicist Yuly Khariton (Khariton, Yuly Borisovich)'s direction on a thermonuclear bomb project. One bomb design, known as the Sloika (“Layer Cake”), was successfully tested on Aug. 12, 1953. Tamm was elected a full member of the Academy of Sciences in October 1953 and the same year was awarded a Hero of Socialist Labour. On Nov. 22, 1955, the Soviet Union successfully tested a more modern thermonuclear bomb that was analogous to the design of the American physicists Edward Teller (Teller, Edward) and Stanislaw Ulam (Ulam, Stanislaw Marcin).