Gamow was born in the city of Odessa, Russian Empire (now in Ukraine) to mixed Russian-Ukrainian parents. He was educated at the Novorossiya University in Odessa (1922–23) and at the University of Leningrad (1923–1929). Gamow studied under Alexander Friedmann for some time in Leningrad, though Friedmann died in 1925. At the University Gamow made friends with three other students of theoretical physics, Lev Landau, Dmitri Ivanenko, and Matvey Bronshtein (who was arrested in 1937 and executed in 1938 by the Soviet regime). The four formed a group known as the Three Musketeers which met to discuss and analyze the ground-breaking papers on quantum mechanics published during those years.

On graduation, he worked on quantum theory in Göttingen, where his research into the atomic nucleus provided the basis for his doctorate. He then worked at the Theoretical Physics Institute of the University of Copenhagen, from 1928 to 1931, with a break to work with Ernest Rutherford at the Cavendish Laboratory, Cambridge. He continued to study the atomic nucleus (proposing the "liquid drop" model), but also worked on stellar physics with Robert Atkinson and Fritz Houtermans.

In 1931 Gamow was elected a corresponding member of the Academy of Sciences of the USSR at age 28 — one of the youngest in the history of this organization. (The youngest corresponding member elected to the Academy of Sciences of the USSR was the outstanding Armenian mathematician Sergey Mergelyan, elected at age 24.) During the period 1931-1934, George Gamow worked in the Physical Department of the Radium Institute (Leningrad) headed by Vitaly Khlopin. Under the guidance and direct participation of Igor Kurchatov, Lev Mysovskii and George Gamow, Europe's first cyclotron was built. In 1932, George Gamow and Lev Mysovskii submitted a draft for consideration by the Academic Council of the Radium Institute, which approved it, and in 1937 the cyclotron was completed..

In the early 1900s, radioactive materials were known to have characteristic exponential decay rates or half lives. At the same time, radiation emissions were known to have certain characteristic energies. By 1928, Gamow had solved the theory of the alpha decay of a nucleus via tunnelling, with mathematical help from Nikolai Kochin. The problem was also solved independently by Ronald W Gurney and Edward U Condon. Gurney and Condon did not, however, achieve the quantitative results achieved by Gamow. Classically, the particle is confined to the nucleus because of the high energy requirement to escape the very strong potential. Also classically, it takes an enormous amount of energy to pull apart the nucleus. In quantum mechanics, however, there is a probability the particle can tunnel through the potential and escape. Gamow solved a model potential for the nucleus and derived from first principles a relationship between the half-life of the alpha-decay event process and the energy of the emission, which had been previously discovered empirically, and was known as the Geiger-Nuttall law.

Gamow then worked at a number of Soviet establishments before deciding to flee Russia because of increased oppression. His first two attempts to defect with his wife, Lyubov Vokhminzeva, were in 1932 and involved attempting to kayak: first a 250-kilometer paddle over the Black Sea to Turkey and then from Murmansk to Norway. Poor weather foiled both attempts. In 1933, the two tried a less dramatic approach - Gamow managed to obtain permission for himself and his wife (who was also a physicist) to attend the Solvay Conference for physicists in Brussels. The two attended and promptly defected. In 1934, they moved to the United States. He began working at The George Washington University in 1934, where he published articles with Edward Teller, Mario Schenberg and Ralph Alpher. Gamow became a naturalized American in 1940.

Gamow produced an important cosmogony paper with his student Ralph Alpher, which was published as "The Origin of Chemical Elements" (Physical Review, April 1, 1948). This paper became known as the Alpher-Bethe-Gamow theory. Gamow had the name of Hans Bethe listed on the article as "H. Bethe, Cornell University, Ithaca, New York" to make a pun on the first three letters of the Greek alphabet, alpha, beta and gamma. Bethe had no other role in the α-β-γ paper.

The paper outlined how the present levels of hydrogen and helium in the universe (which are thought to make up over 99% of all matter) could be largely explained by reactions that occurred during the "big bang". This lent theoretical support to the Big Bang theory, although it did not explain the presence of elements heavier than helium (this was done later by Fred Hoyle).

In this paper, no estimate of the strength of the present day residual cosmic microwave background radiation (CMB) was made. Shortly thereafter, Alpher and Robert Herman predicted that the afterglow of the big bang would have cooled down after billions of years, filling the universe with a radiation five degrees above absolute zero.

Gamow published another paper in the British journal Nature in 1948, in which he developed equations for the mass and radius of a primordial galaxy (which typically contains about one hundred billion stars, each with a mass comparable with that of the sun).

Astronomers and scientists did not make any effort to detect this background radiation at that time, due to both a lack of interest and the immaturity of microwave observation. Consequently, Gamow's prediction in support of the big bang was not substantiated until 1964, when Arno Penzias and Robert Wilson made the accidental discovery for which they were awarded the Nobel Prize in Physics in 1978. Their work determined that the universe's background radiation was 2.7 degrees above absolute zero, just 2.3 degrees lower than Gamow's 1948 prediction.