The three-match series, the first bilateral between the neighbours, will be played in Sharjah on March 24, 26 and 27
Ravindra Jadeja celebrated his return to international cricket with a five-wicket haul as India bowled out Australia for 177 and then cruised to 77-1 to dominate day one of the opening Test in Nagpur on Thursday.
Home captain Rohit Sharma led India's robust reply with a typically belligerent 56 not out that included nine boundaries.
Nightwatchman Ravichandran Ashwin was yet to open his account at the other end but India would be pressing for a decisive first-innings lead in the contest when play resumes on Friday.
Earlier, Australia skipper Pat Cummins won the toss and elected to bat on a spin-friendly pitch but the tourists had both their openers back in the hut inside the first 13 deliveries.
Mohammed Siraj trapped Usman Khawaja lbw with his first delivery, an outswinger that struck the opener low on his pad.
In the next over, Mohammed Shami sent David Warner's off-stump cartwheeling to reduce Australia to two for two.
Marnus Labuschagne (49) and Steve Smith (37) staged a mini-recovery with a 82-run stand but the home spinners were in the thick of things after the lunch break.
Australia scored 98 runs in that session but also lost six wickets with Jadeja as the wrecker-in-chief, while off-spinner Ashwin (3-42) played the second fiddle.
Left-arm spinner Jadeja lured Labuschagne out of the crease to be stumped and dismissed Matt Renshaw for a first-ball duck with the next delivery to be on a hat trick.
While that feat eluded him, Jadeja claimed the crucial wicket of Smith with an extra delivery he had to bowl for having sent down a no-ball earlier in that over.
Alex Carey realised the futility of trying to hang around and decided to counter-attack.
Carey hit seven boundaries in his 36 but his 33-ball cameo ended after he fluffed a reverse sweep against Ashwin, who became the second Indian bowler - after Anil Kumble -- to claim 450 test wickets.
Todd Murphy scored a duck in his debut Test and Peter Handscomb, picked ahead of Travis Head, made 31 before falling to Jadeja who claimed 5-47 in his return from a knee injury suffered last year.
"I was looking to bowl into the stumps because there was no bounce on the wicket," Jadeja told the official broadcasters.
"So I was targeting the stump-to-stump line and that helped me.
"The odd ball was spinning and the odd ball was going straight, so that is what I was looking to do."
His captain Rohit gave an early indication of India's batting approach hitting counterpart Cummins for three boundaries in the first over of the innings.
Murphy broke the flourishing 76-run opening stand when he took a return catch to remove KL Rahul (20) for his maiden Test wicket.
For India, Suryakumar Yadav, the top-ranked Twenty20 batter, made his Test debut alongside wicketkeeper KS Bharat.
Delhi, Dharamsala and Ahmedabad host the other matches of the four-Test series.
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