Teller was from a family of prosperous Hungarian Jews. After attending schools in Budapest, he earned a degree in chemical engineering at the Institute of Technology in Karlsruhe, Germany. He then went to Munich and Leipzig to earn a Ph.D. in physical chemistry (1930). His doctoral thesis, on the hydrogen molecular ion, helped lay the foundation for a theory of molecular orbitals that remains widely accepted today. While a student in Munich, Teller fell under a moving streetcar and lost his right foot, which was replaced with an artificial one.

During the years of the Weimar Republic, Teller was absorbed with atomic physics, first studying under Niels Bohr (Bohr, Niels) in Copenhagen and then teaching at the University of Göttingen (1931–33). In 1935 Teller and his bride, Augusta Harkanyi, went to the United States, where he taught at George Washington University in Washington, D.C. Together with his colleague George Gamow (Gamow, George), he established new rules for classifying the ways subatomic particles can escape the nucleus during radioactive decay. Following Bohr's stunning report on the fission of the uranium atom in 1939 and inspired by the words of President Franklin D. Roosevelt (Roosevelt, Franklin D.), who had called for scientists to act to defend the United States against Nazism, Teller resolved to devote his energies to developing nuclear weapons.

By 1941 Teller had taken out U.S. citizenship and joined Enrico Fermi (Fermi, Enrico)'s team at the University of Chicago in the epochal experiment to produce the first self-sustaining nuclear (Manhattan Project) chain reaction. Teller then accepted an invitation from the University of California at Berkeley to work on theoretical studies on the atomic bomb with J. Robert Oppenheimer (Oppenheimer, J. Robert); and when Oppenheimer set up the secret Los Alamos Scientific Laboratory in New Mexico in 1943, Teller was among the first men recruited. Although the Los Alamos assignment was to build a fission bomb, Teller digressed more and more from the main line of research to continue his own inquiries into a potentially much more powerful thermonuclear hydrogen fusion bomb. At war's end he wanted the U.S. government's nuclear weapons development priorities shifted to the hydrogen bomb (thermonuclear bomb). Hiroshima, however, had had a profound effect on Oppenheimer and other Manhattan Project scientists, and few had the desire to continue in nuclear weapons research.

Teller accepted a position with the Institute for Nuclear Studies at the University of Chicago in 1946 but returned to Los Alamos as a consultant for extended periods. The Soviet Union's explosion of an atomic bomb in 1949 made him more determined that the United States have a hydrogen bomb, but the Atomic Energy Commission's general advisory committee, which was headed by Oppenheimer, voted against a crash program to develop one. The debate was settled by the confession of the British atomic scientist Klaus Fuchs that he had been spying for the Soviet Union since 1942. Fuchs had known of the American interest in a hydrogen bomb and had passed along early American data on it to the Soviets. In response, President Harry Truman ordered the go-ahead on the weapon, and Teller laboured on at Los Alamos to make it a reality.

Teller was subsequently credited with developing the world's first thermonuclear weapon, and he became known in the United States as “the father of the H-bomb.” Ulam's key role in conceiving the bomb design did not emerge from classified government documents and other sources until nearly three decades after the event. Still, Teller's stubborn pursuit of the weapon in the face of skepticism, and even hostility, from many of his peers played a major role in the bomb's development.

At the U.S. government hearings held in 1954 to determine whether Oppenheimer was a security risk, Teller's testimony was decidedly unsympathetic to his former chief. “I would feel personally more secure,” he told the inquiry board, “if public matters would rest in other hands.” After the hearings' end, Oppenheimer's security clearance was revoked, and his career as a science administrator was at an end. Although Teller's testimony was by no means the decisive factor in this outcome, many prominent American nuclear physicists never forgave him for what they viewed as his betrayal of Oppenheimer.

Teller was instrumental in the creation of the United States' second nuclear weapons laboratory, the Lawrence Livermore Laboratory, in Livermore, California, in 1952. For almost the next four decades it was the United States' chief factory for making thermonuclear weapons. Teller was associate director of Livermore from 1954 to 1958 and from 1960 to 1975, and he was its director in 1958–60. Concurrently he was professor of physics at the University of California at Berkeley from 1953 to 1960 and was professor-at-large there until 1970.

A staunch anticommunist, Teller devoted much time in the 1960s to his crusade to keep the United States ahead of the Soviet Union in nuclear arms. He opposed the 1963 Nuclear Test Ban Treaty, which banned nuclear weapons testing in the atmosphere, and he was a champion of Project Plowshare, an unsuccessful federal government program to find peaceful uses for atomic explosives. In the 1970s Teller remained a prominent government adviser on nuclear weapons policy, and in 1982–83 he was a major influence in President Ronald Reagan (Reagan, Ronald W.)'s proposal of the Strategic Defense Initiative, an attempt to create a defense system against nuclear attacks by the Soviet Union. In 2003 Teller was awarded the Presidential Medal of Freedom.