"I had an x-ray (on Monday) and the doctor is very happy with my progress," Warne told Melbourne's Herald Sun newspaper.
The right-arm bowler broke his left hand earlier this month while batting for English county side Hampshire, raising doubts over his fitness for the upcoming series.
"I will be fine to play. The hand will still be sore for a while and I will probably have a bit of discomfort, but it will not stop me from performing my usual duties."
One of Wisden's five cricketers of the 20th century, Warne is 10 wickets behind Muttiah Muralitharan's world record mark of 527 wickets and has a chance to move ahead of the Sri Lankan in the series.
Last week, Muralitharan withdrew from the Australia tour for personal reasons following an investigation into his bowling action that prompted Australian Prime Minister John Howard to call him a "chucker".
The 34-year-old Warne said on Tuesday he would be able to bowl and bat as normal and field in his regular position in slips.
Sri Lanka's opening tour match against a Northern Territory XI in Darwin starts on June 24. The first Test starts in Darwin on July 1.
