Set a formidable target of 324 in their second innings of the third and final Test, Australia collapsed were all out for just 160 as Herath took seven for 64 at the Sinhalese Sports Club (SSC) in Colombo.
It was the third time in a row that the Australians had lost all of their Tests in away series against teams from the sub-continent and allowed India to regain the number one slot in the world rankings.
And it was the first time that the hosts had ever recorded a clean sweep of a major cricketing nation since they gained Test status in 1981.
“It’s a hard one to grasp really, it’s been a very tough series again, that is the our third straight whitewash loss in the subcontinent,” a disappointed Australian skipper Steve Smith told reporters.
“Can’t fault the prep, got here early, worked as hard as we can. Think Sri Lanka have played some great cricket, (it’s) disappointing but a great learning curve.”
Openers David Warner and Shaun Marsh briefly raised Australian hopes of a consolation win as they made a brisk start to their chase before their partnership was broken just before lunch with the score on 77.
Off-spinner Dilruwan Perera’s dismissal of Marsh, who scored a century in the first innings in Colombo, was the cue for a dramatic collapse by the Australians who lost their last nine wickets for just 60 runs.
The destroyer-in-chief was Herath who, having claimed six wickets in the first innings, was again close to unplayable at times.
Smith was his first victim and he then snared Adam Voges in the same over.
Warner, who had batted well for his 68 with six fours and a six, was Perera’s second big strike.
His removal opened up the tail to Herath who wrapped up proceedings by taking the final wicket of Nathan Lyon, triggering wild celebrations in front of a raucous home crowd — many of whom had been admitted for free.
“The feeling is unbelievable. This is one of the top series for us,” a beaming Sri Lankan skipper Angelo Mathews after being handed the Warne-Muralitharan Trophy.
Earlier Sri Lanka, who resumed on 312 for eight, declared their second innings on 347 for eight with overnight batsman Dhananjaya de Silva unbeaten on 65.
Playing in just his third Test, de Silva smashed 10 boundaries during his 74-ball knock, after scoring a century in the first innings.
Kaushal Silva’s gritty 115 played a big part in Sri Lanka registering their first series sweep against a major side since gaining Test status in 1981.
Defiant centuries from Dinesh Chandimal and Dhananjaya de Silva ensured that the hosts got a decent first-innings score of 355.
The batting duo put together a defining 211-run stand for the sixth wicket after the hosts were left reeling at 26 for five having elected to bat.
“What a moment … credit to de Silva the way he batted and then Chandimal the way they got us through the second and third sessions on the first day and then Herath, doing his thing,” Mathews said.
Australian paceman Mitchell Starc was the standout performer for the visitors with his 24 wickets in the series including three five-wicket hauls.
But the man-of-series award went to Herath who took a total of 28 wickets in the three Tests, including a hat-trick in the second rubber.
Sri Lanka had only ever beaten Australia once before in a Test match but they won the first two contests of the series comfortably in Pallekele and Galle before the finale in the capital.
The outcome means that India, who have just won an away series against the West Indies, are now top of the rankings and Pakistan have also leapfrogged Australia into second place.
The teams now head into the limited-overs phase of the tour with the first of the five one-day internationals scheduled for August 21.