The 2-1 series win was confirmed when the fifth day of the fourth Test in Sydney was washed out by rain and the match was drawn.

"I've never been more proud of being part of a team," said Kohli.

"By far, this is my biggest achievement. The series win will give us a different identity."

Test cricket is most important - Kohli

Australia went into the final day of the series with little hope of achieving the victory they needed to win the Test and draw the series.

They were due to resume their second innings on 6-0, having been forced to follow on at home for the first time in 30 years after being bowled out for 300 in reply to the tourists' first-innings total of 622-7 declared.

But no play was possible and India, who first toured Australia in 1947-48, celebrated a famous victory.

"It's a proud moment. More so because for the last 12 months we understand what we have gone through as a team," said Kohli.

"The fact that the reward has come in the most historic series for Indian cricket is the cherry on the top of the cake.

"In the 10 years that I have played, it is the proudest moment that I have experienced and we're so happy for the whole team.

"It is a young bunch of guys and to have that belief to keep striving for excellence on a daily basis and to get a reward like this we definitely have to be happy."

He added: "We definitely want to build on this and always promote the message of Test cricket being the most important and the most valued format of the game, which it rightfully is.

"From where I see it, this is our vision for Indian cricket."

We were outplayed - Paine

Australia struggled without batsmen Steve Smith and David Warner, who are serving a 12 month ban for the ball-tampering controversy in South Africa last March.

No Australia player managed to score a century in the series, while India managed five - three of those coming from Cheteshwar Pujara, who scored 521 runs.

"We have to tip our hat to India, we know how tough it is to win in Australia so congrats to Virat and (coach) Ravi (Shastri) because it's a huge achievement," said Australia captain Tim Paine.

"We are disappointed, definitely over the last two Tests. We had our chances in Adelaide, and in Perth I thought we played some good cricket, but in Melbourne and Sydney, we've been outplayed."

He added: "It's been great for some guys to get some experience in international cricket, particularly the top six, against potentially the best pace bowling attack in the world at the moment. So they are going to learn a lot from that."