Rohit, known as the "Hitman" for his big hundreds and six-hitting, this month led the team to a one-day series sweep over the West Indies.
He has led IPL side Mumbai Indians to a record five titles, and had already taken over the white-ball captaincy following Kohli's surprise departure.
Always a frontrunner to take over the Test duties, Rohit has been a regular member of the Test team since opening the batting for India in October 2019, when he hit twin centuries.
The swashbuckling batsman, a white-ball star, has scored 3,047 runs including eight centuries in 43 Tests since making his debut in 2013.
His attacking batting and penchant for big scores -- he scored 177 on his Test debut and has a top score of 212 -- make him a favourite with the fans.
Critics though highlight Rohit's injury-prone career and the fact that he is 18 months older than Kohli, meaning he may prove to be a stopgap skipper before someone younger -- such as Rishabh Pant -- takes over.
His ample physique also contrasts with lean fitness fanatic Kohli, but selection chairman Chetan dismissed concerns about the new captain.
"Today's professional cricketers manage their body and Rohit has no problem at all and he is absolutely okay," he said.
"And if such a big and experienced cricketer comes forward and becomes captain then the future captains to be groomed under Rohit would be a tremendous thing for us."
Pace bowler Jasprit Bumrah was named as Rohit's Test deputy, putting him in contention to become the next skipper.
Rohit is seen as less combative than his predecessor, who had frequent run-ins with opposing teams and umpires.
Under Kohli, one of the best batsmen of his generation, India rose up the international rankings and shed their reputation for performing poorly away, winning two series in Australia.
The first Test against Sri Lanka at Mohali on March 4 is set to be his 100th game in the five-day format.
He finished with 40 wins and 17 losses in 68 Tests as captain -- by far the best percentage of any Indian skipper, well ahead of predecessor MS Dhoni.
But under him India failed to win a single international championship, including a disastrous T20 World Cup last year, eroding his popularity with fans and the cricket board, the BCCI.
Kohli, married to Bollywood star Anushka Sharma, has been enthusiastic in his support of Hindu nationalist prime minister Narendra Modi on Twitter, where he has over 45 million followers.
Nonetheless last year he was trolled by Hindu hardliners for defending the team's only Muslim player Mohammed Shami after the team's World Cup thrashing by Pakistan.
"Attacking someone over their religion is the most pathetic thing that a human being can do," Kohli said.
Kohli's batting form has also fallen off, with his last century dating back to August 2019 and scoring just eight, 18 and nought in the recent one-day series against the West Indies.
"I've done the job with absolute honesty and left nothing out there," Kohli said after quitting as Test captain.