His critics will argue that his decision, which was widely anticipated, was long overdue. Mr Bradley, whose shrewdness and inscrutable style earned him the nickname 'The Sphinx', will leave a mixed legacy.
Mr Bradley, who was the first black to become mayor of a big US city, is the latest in a flurry of departures following the riots, which were ignited when a jury failed to convict four white police officers accused of beating a black motorist, Rodney King. Daryl Gates, the city's notoriously outspoken police chief, has been replaced by Willie Williams, the first black to head the Los Angeles Police Department. Ira Reiner, the district attorney whose office was responsible for the officers' bungled prosecution, has suddenly abandoned his battle for re-election in November. The old guard of Los Angeles appears to be stepping aside.
The son of a Texas sharecropper, Tom Bradley was born into a society where poverty and racism were the norm, but which he escaped, assisted by an extraordinary capacity for work and intense ambition. He became a college track star, a lieutenant in the police force, a lawyer, and, finally, the city's first elected black councilman and mayor. Announcing his retirement, he said triumphantly: 'The people who said that a black man couldn't go to college, couldn't rise through the ranks of the police department, and couldn't attain the highest public offices were wrong.'
Mr Bradley, a tall, fit and aloof man, will be credited with the development of Los Angeles into a Pacific Rim international trading centre and the nation's busiest cargo port. In the last two decades the city's run-down centre has sprouted skyscrapers, monuments to the money he helped attract. His tenure saw the successful 1984 Olympics, radical clean-air initiatives, and the city's first steps towards a mass-transit system.
His administration was increasingly accused of stagnating. There were accusations of conflict of interest which led to several lengthy ethics investigations. The most serious instance came in 1988, when the chairman of the Far East National Bank paid him dollars 18,000 (pounds 11,000) as a special adviser at a time when the bank was seeking city deposits. Although Mr Bradley was cleared, mutterings about his methods continued behind the scenes.
Mr Bradley was also at the centre of one of the most epic enmities in the city's history. Neither he nor his police chief, Mr Gates, could stand each other. They were not on speaking terms for months before the riots. But, for all his criticism of Mr Gates, the mayor was himself censured by the Christopher Commission investigation into the force. It found him guilty of failing to exert influence over the police, for years riddled with brutality and racism.