Praise and congratulations poured in for Virat Kohli's India on Monday after the tourists won their first-ever Test series in Australia, underlining their world number one ranking.

India clinched the series 2-1 after the fourth and final Test was called off due to rain in Sydney, confirming their first win in Australia since they began touring Down Under in 1947-48.

"A historic cricketing accomplishment in Australia!" Prime Minister Narendra Modi wrote on his official Twitter handle.

"Congratulations to the Indian Cricket Team for the hard-fought and richly deserved series victory.

"The series witnessed some memorable performances and solid teamwork. Best wishes for the various games ahead."

Batting legend Sachin Tendulkar called it "an amazing day for Indian cricket. #TeamIndia has made this a series to be cherished. Proud of the boys."

He singled out for praise Cheteshwar Pujara after his 521 runs in four matches -- including 193 in Sydney -- won him man of the series.

"Test match batting at its best by Pujara. @cheteshwar1 has been the difference between the 2 teams for me. To be able to bat for such long periods of time is a testament to his concentration and understanding of the game," Tendulkar wrote on Twitter after Pujara's Sydney knock.

Paceman Jasprit Bumrah remained the highest wicket-taker with 21 wickets alongside Aussie spinner Nathan Lyon, and Kohli insisted the achievement was due to a complete team effort.

"So proud to be a part of this team, great feeling! This is not just a team this is a family. Onwards and upwards from here on," Kohli said on Twitter.

Former greats VVS Laxman and Virender Sehwag also lauded the win, crediting every member of the current squad.

Laxman said the win "gives such an immense sense of satisfaction and joy", while Sehwag felt "proud" of the team's achievement.

Former skipper Sunil Gavaskar rejected claims that India won because Australia was weakened by the absence of the suspended Steve Smith and David Warner.

"India played the opposition they were presented with and it's a great achievement for them," Gavaskar said during a post-match show on host broadcasters Sony Six.