The off-spinner, playing his 116th Test, bowled Paul Collingwood to grab his fifth wicket in the innings and surpass retired Australian leg-spinner Warne's world record tally of 708 wickets in 145 matches.
"I congratulate Murali for breaking the record I had," Warne said Monday.
"I knew I would only have it for a short time. Murali has said he wanted to take 1000 Test wickets and he has every chance of getting there.
"If he does I don't think anyone else will catch him.
Muralitharan's career has been blighted by concerns over the legitimacy of his action but Warne refused to denigrate the achievement.
"Despite what people say he'll be remembered as one of the game's great bowlers," Warne said.
"He's an excellent competitor and has been great for Sri Lankan cricket. He's a great bloke too. I've been to Sri La