After completing an eight-wicket victory in the fourth Test in Dharamsala, to seal the series 2-1, India will remain number one in the ICC rankings at the cut-off date of April 1.
They will therefore also win the table-toppers' prize of $1million.
India needed only another 87 runs on the fourth morning, chasing just 106 in all after bowling Australia out for 137.
The hosts duly knocked off the remaining runs as KL Rahul finished unbeaten on 51 in an unbroken stand with Ajinkya Rahane, after Australia had taken two wickets in the seventh over of the day.
Murali Vijay fell with the score on 46 when he nicked a moving ball from Pat Cummins and Cheteshwar Pujara needlessly ran himself out for a duck five balls later.
But a 61-run stand followed off 59 balls, with Rahul going past 50 as he hit the winning runs.
Kohli could reflect with satisfaction after India had continued their long winning run on home soil, since England last beat them in a series there in 2012.
He said: "The longest format of the game really tests a team's character, and I'm proud that we have proved ourselves to be the best.
"We are absolutely delighted to have topped the ICC Test rankings.
"We have maintained our position with some really good cricket in recent months. The team has shown the tenacity to bounce back from difficult situations."
The next Test assignment for Steve Smith's Australia will be the 2017/18 Ashes, beginning in November.