The unanimous verdicts immediately eased tensions in a city that has been living in fear of a repetition of last year's deadly riots, which erupted when a state court in California acquitted the officers on almost every charge.
The verdicts were announced at 7am - an hour clearly chosen in order to reduce the risk of violence - as thousands of Los Angeles police flooded the streets and troops from the state militia were placed on stand-by in case of trouble. The jury ruled that Sgt Stacey Koon, 42, who supervised the beating, was guilty of violating Mr King's civil rights by permitting the use of excessive force against him. Officer Laurence Powell, 30, who struck Mr King dozens of times with his metal baton, was convicted of violating those rights, but acquitted of a lesser charge.
Timothy Wind, 32, a trainee officer under Powell's supervision, was acquitted, despite striking Mr King at least 12 times. A fourth officer, Theodore Briseno, 40, who kicked Mr King once and later condemned the beating as excessive, was also found not guilty.
President Bill Clinton said the case was a tribute to the US legal system and 'established what a lot of people had felt in their hearts for two years - that the civil rights of Rodney King were violated'. Black community leaders also gave a broadly favourable reaction to the verdicts, which came more than two years after an amateur cameraman filmed Mr King, who is black, being repeatedly kicked and beaten by white officers as several dozen police looked on. Mr King, 28, a parolee, was stopped after a late- night car chase.
There were highly emotional scenes yesterday at the First African Methodist Episcopal Church in South Central Los Angeles, where hundreds had gathered to hear the verdicts. Cheers erupted when the guilty decisions were announced. The Rev Jesse Jackson said he felt a 'sense of relief' in the court's decision, which he said was 'a restoration of confidence in the judicial system'.
A tearful Rev Cecil Murray, the city's most powerful black churchman, said he was surprised and pleased: 'It defuses the tension here to a great extent.' In South Central Los Angeles a young black youth was seen dancing in the streets, shouting 'Yeah, yeah. We got two of them'.
The jury in the federal trial, who included two blacks, a Hispanic and nine whites, spent 40 hours deliberating - eight more than the panel of non-blacks who acquitted the officers last year in a trial held in a mainly white suburb outside Los Angeles.
The two convicted face up to 10 years in prison, and a dollars 250,000 ( pounds 160,000) fine. They will return to court for sentencing on 4 August, but will remain free until then. None of them gave any immediate reaction; three have signed contracts with a US television show.
Although the city was calm, its chief of police, Willie Williams, mobilised the best part of his 7,610-strong force before the verdicts, sending thousands of extra officers on to the streets. The National Guard had 600 troops stationed in armouries in the city.
Further reports, page 3