The off-spinner, playing his 116th Test, bowled Paul Collingwood in the morning session of the third day of the first Test against England here to grab the record in his home town.
The 35-year-old's achievement was watched by about 6,000 joyous fans at the Asgiriya stadium, including his parents and Indian wife Madhimalan.
The feat marks a new high in the 15-year career of one of the most celebrated bowlers of the modern game whose controversial bent-arm action was questioned in the past by umpires.
Muralitharan had previously held the record briefly in 2004 when he overtook West Indian fast bowler Courtney Walsh's 519-wicket mark, before Warne surpassed him.
Muralitharan's 61st five-wicket haul -- he finished with 6-55 to take his tally to 710 -- saw England being bowled out for 281 on the third morning in reply to Sri Lanka's first innings total of 188.
The beaming Sri Lankan told a television interviewer during the lunch break that "it was the right time" to achieve the record.
"It's my hometown, my parents are here, my wife is here, all the relatives are here and all my schoolfriends," said Muralitharan.
"It's a bigger moment than if I had taken it in Australia. It's the right time, I think. It's not easy to take six wickets in an innings but I managed to let my pressure off now."
Muralitharan said bowling Collingwood was a special moment, even though the ball did not spin as much as he had expected.
"I tried to spin the ball and it went the other way, but that's a special wicket," he said.
Muralitharan said he regarded the 16 wickets he took against England at the Oval in 1998 as his best performance.
"That was the highlight because it made people think that I was a good bowler and one who could take wickets overseas as well as at home," he said.
Muralitharan's bent-arm action, the result of an elbow deformity since birth, helped him impart considerable turn and bounce even on the most placid wickets.
The unusual action caused heartburn in the cricket world, especially in Australia where umpires no-balled him for throwing and former prime minister John Howard once called him a "chucker."
Sri Lanka's captain Mahela Jayawardene saluted his master spinner, saying Murali was not only "the best bowler in the world" but also the ideal team-mate.
"He is hungry for wickets but for him the team comes first," Jayawardene told AFP.
"At team meetings, he always talks about how to get the opposition out, how to win matches. It is always about the team, never about how we get another record.
"With that attitude, he will go on for a long, long time."
Murali, who made his Test debut in 1992, hopes to carry on despite a string of injuries that once forced exasperated former team physio Alex Kontouris to describe him as a "bio-mechanical mess."
He said in a recent interview he wants to take 1,000 Test wickets and hopes to play for Sri Lanka till the 2011 limited-overs World Cup to be hosted in the Indian sub-continent.
"I want to achieve a little bit more because I am still hungry for wickets," Muralitharan said.
Warne, paying rich tributes to his fellow-spinning great, said in Australia that Muralitharan's record will stand for ever.
"I congratulate Murali for breaking the record I had," said Warne.
"Murali has said he wanted to take 1000 Test wickets and he is every chance of getting there.
"If he does I don't think anyone else will catch him.
"Despite what people say he'll be remembered as one of the game's great bowlers."