Elaine Ray, a spokeswoman for the Stanford University news service, said Teller had suffered a stroke earlier this week and died at his home on the university campus on Tuesday.
A naturalised US citizen born in Hungary, Teller was a key member of a group of top scientists who fled Hitler's Germany and ended up working on the Manhattan Project, the secret programme that developed the atomic bomb.
After the war, Teller pressed the case for a continued strong national defence, persuading President Harry Truman of the need for the far more powerful hydrogen bomb.
The US detonated the first H-bomb on the Pacific atoll of Eniwetok in November 1952. It was 2500 times more powerful than the atomic weapons dropped on Hiroshima and Nagasaki in 1945.
"It wasn't a choice. Nuclear energy existed," Teller told a newspaper interviewer shortly before his 80th birthday. "We would have found it no matter what we did. It's sheer arrogance to say we created the bomb."
"Edward Teller was one of the world's leading scientific minds of the 20th century, and he made a major contribution to the security of our nation and world peace," University of California President Richard C Atkinson said.
Born in Budapest in 1908, Teller completed his PhD in physics under Werner Heisenberg in 1930 at the University of Leipzig, and did post-graduate work in Copenhagen with pioneering Danish nuclear physicist Neils Bohr.
"It wasn't a choice. Nuclear energy existed. We would have found it no matter what we did. It's sheer arrogance to say we created the bomb"
Teller was director of the Livermore lab from 1958 to 1960 and professor of physics at the University of California from that time until his retirement in 1975.
Teller said he regretted Truman's decision to drop the A-bomb on Japanese cities, saying he felt the weapon should have been tried first in a demonstration in hopes Japan's leaders would have been impressed enough to end the war.
He came under fire in the 1980s when he helped convince President Ronald Reagan that the United States should spend billions of dollars on a space-based defence umbrella that came to be known as "Star Wars."
Critics said the system, based partly on laser-equipped satellites designed to shoot down enemy missiles, was unfeasible and too expensive. Teller won the day, but the ambitious defence umbrella remains a work in progress.