The prolific wicket-taker refused to come on Sri Lanka's last tour here in 2004 because of constant "no-ball" chants by Australian crowds. He was also labelled a "chucker" by Prime Minister John Howard.
It was a low-point in a frosty cricket relationship with Australia which began when he was called for throwing by Australian umpire Darrell Hair in the Melbourne Boxing Day Test in 1995.
But Muralitharan arrived with the 16-man squad here on Monday for the One-day tri-series with Australia and South Africa and Atapattu said the champion spinner had no qualms about coming this time.
"He's willing to give 100 percent for me and the team," Atapattu told reporters Tuesday.
Atapattu said it was clear Australia's response to the 2004 Boxing Day tsunami, particularly a fund-raising match Muralitharan was part of in Melbourne last year, caused his change of heart.
"He said he wouldn't tour Australia when we toured here for the two Test matches," Atapattu said.
"The tsunami game turned corners for him, I think it made him think differently."
Muralitharan was also part of the World XI Test and one-day teams which played against Australia in Sydney and Melbourne last October.
Sri Lankan coach Tom Moody urged Australian crowds to end the "no-ball" chants.
"It's not ideal and it's a shame that it happens, particularly since he's gone through every test and scrutiny a player could possibly go through," Moody said.
"We just need to enjoy the special talent he's got and let the game progress."
Sri Lanka play Victoria on Wednesday in their only warm-up match before the tri-series opener against Australia here on Friday.
The tourists would appear to have their work cut out against the world champion Australians, having won just two of their past 11 ODI matches.
They beat New Zealand on Monday in their last outing, their only win of a five-game series against the Kiwis.