Indian players celebrate after winning the Border Gavaskar Trophy test series. Reuetrs
The hosts won the series 2-1 and the world's two top-ranked teams will do battle again on June 7-11 at The Oval in the World Test Championship final.
Even before the players shook hands on day five, India knew they had reached the WTC decider thanks to New Zealand's thrilling last-ball win over Sri Lanka earlier in the day.
It will be India's second successive WTC final, having lost the inaugural edition to New Zealand in 2021.
Australia reached 175-2 in their second innings in the final session of play at the world's biggest cricket stadium when the players of both teams called it a day.
"We do understand the importance of this series and the opposition. Lot of hard work has gone into this," India skipper Rohit Sharma said.
Coach Rahul Dravid told broadcaster Star Sports: "It was a really hard-fought series, there were moments where we were put under extreme pressure by a really good cricket team and we responded."
India similarly lifted the Border-Gavaskar Trophy at home in 2017 and then beat the Australians in their own back yard in 2018-19 and 2020-21, each time 2-1.
Travis Head (90) and Marnus Labuschagne (63 not out) snuffed out India's push for a victory on the final day with a stand of 139 after nightwatchman Matthew Kuhnemann fell early for six.
The left-handed Head, capping a successful series after being left out of the first Test, missed out on his century after being bowled by Axar Patel.
Regular opener Usman Khawaja did not to bat due to "lower leg soreness" after getting hurt while fielding on day four.
The match in Ahmedabad belonged though to Kohli, who hit a masterful knock on day four to end a Test century drought of 1,205 days since his previous ton.
The marathon 364-ball knock blocked every chance of a potential defeat for the hosts after Australia posted 480 on a vastly different pitch from the previous three Tests.
Expectations and more
Kohli, one of the best players of his generation, recorded his 28th Test century to power India to 571 all out on Sunday as India managed a lead of 91 after their first innings.
"I think in Test cricket I wasn't able to play with my tempo and template that I have played with for the last 10 years for a while now," said the man-of-the-match.
Kohli's partnership of 162 for the sixth wicket with Axar, who hit his third half-century of the series with an attacking 79, marked India's dominance on Sunday.
Opener Shubman Gill hit 128 to lead India's reply and make the most of his opportunity after being added to the team in place of struggling KL Rahul in the third Test.
Indian spinner Ravichandran Ashwin excelled with his six wickets in Australia's first innings, in a run-filled match which was at odds with the first three Tests.
Ashwin managed 25 wickets in the series, ahead of Ravindra Jadeja's 22, as the spin duo received the player-of-the-series award jointly.
Not to be outdone, Australian spinner Nathan Lyon took 22 wickets including three in the final Test and was ably supported by up-and-coming spinners Todd Murphy and Kuhnemann.
"The spinners bowled really well," said stand-in-skipper Steve Smith.
"Murphy and Kuhnemann bowled with composure. Lyon bowled his best in the first innings here, the best I have seen him bowl."
An Australia team which lost several players to injury and personal circumstances had appeared on the brink of chaos after being well beaten inside three days in the first two Tests.
But the tourists roared back to win the third match in Indore in just over two days on a viciously turning track to keep the series alive until the final match.
Smith led Australia in the final two Tests after regular captain Pat Cummins returned home to be with his seriously ill mother. She died last week.
The two teams now head into three one-day internationals starting Friday in Mumbai, ahead of the 50-over World Cup in India later this year.
Washington Sundar and Shardul Thakur, in just his second Test, put on 123 runs for the seventh wicket — a record for India at the Gabba — taking their team from a precarious 186 for seven to 309 before Thakur was bowled by Pat Cummins for an entertaining 67.
Pucovski rode his luck for his 62 but his partnership of 100 with Marnus Labuschagne 67 not out for the second wicket established a solid platform for the hosts.
India were 321-7 at stumps with all-rounder Ravindra Jadeja proving his worth for the second straight day of his international return with an unbeaten 66.
The Games, delayed a year due to China's measures to combat the COVID-19 pandemic, will be the country's biggest sporting event in over a decade in several metrics, with around 12,000 athletes from 45 nations competing in 40 sports.
India have become only the second team in men's cricket history to occupy the number one spot across all three formats after defeating Australia in the first ODI on Friday.
The prestigious championships for amateurs and professionals will take place under the patronage of Sheikh Mohammed Bin Hamad Bin Mohammed Al Sharqi, Crown Prince of Fujairah, and will be held at the Zayed Sports Complex.
The total prize money pool is $10 million for the tournament, the same which was given in the 2015 and 2019 editions of the competition. The runners-up of 2023 Men’s ODI World Cup will receive $2 million, while the losing semi-finalists will get $800,000 each.