The Sri Lankans, who won the first and second Test match, beat the visitors by 163 runs at the Sinhalese Sports Club grounds.
Batting first after winning the toss in the five day game, the Sri Lankans scored 355 runs in their first innings with Dinesh Chandimal and Dhananjaya de Silva scoring centuries.
For the Australians Mitchell Starc took five wickets while Nathon Lyon took three wickets.
The Australians then managed to score 379 runs in their first innings with Shaun Marsh and captain Steven Smith scoring hundreds.
Rangana Herath took six wickets. Batting in the second innings Sri Lanka declared on 347 for 8 wickets with Kaushal Silva scoring a century.
In reply Australia fell short of the target in their second innings and made just 160 runs with Herath taking 7 wickets giving Sri Lanka the win and the series.
The Sri Lankans have never won all three Tests in a three match Test series against Australia before the current series.
Rangana Herath was named man of the match. (Colombo Gazette)