The match will go ahead despite the Board of Control for Cricket in India threatening to cancel the match over a financial dispute with the courts.
Lancashire batsman Hameed, 19, will become only the second teenager to play Test cricket for England since 1949.
Ben Duckett, who opened in the recent Test series against Bangladesh, will replace Gary Ballance at four.
"We have all been hugely impressed with the way Haseeb has gone about his business on this tour. Nothing seems to faze him," said captain Alastair Cook.
Hameed, who scored 1,129 runs at an average of 52 in County Championship Division One this summer, was called up for the Test tour of Bangladesh in October but did not play in the 1-1 series draw.
All-rounder Ben Hollioake, who was 19 when he played against Australia in 1997, is the only other teenager to appear in a Test for England since 18-year-old Brian Close made his debut in 1949.
Left-hander Ballance, 26, has been dropped after scoring only 24 runs in four innings in Bangladesh.
"I feel sorry for Gary," said Cook. "They were tough conditions in Bangladesh and ultimately it's about how many runs you score.
"I still think he's a fine player and one who I think will play again for England and do well."
The Board of Control for Cricket in India (BCCI) threatened to cancel the opening Test - the first to be held in Rajkot - unless judges ended a freeze on its bank accounts.
Last month, the supreme court ruled that the board must obtain prior approval from a special panel investigating its governance in order to release funds to state associations which host Tests.
However, the supreme court has released £70,000 so the match can go ahead.
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Cook, 31, will break Michael Atherton's record of 54 Tests as England captain during the opening game of the five-match series.
He hinted in a recent interview with the Cricketer magazine that this series could be his last as captain, but said on Tuesday he was not thinking of anything beyond the India tour.
"I have always said to (England director of cricket) Andrew Strauss we will take every series as it comes," said Cook.
"It could be two months, it could be a year, it could be six months, it could be anything. For me, it's about concentrating on this series."
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Former England captain Michael Vaughan said Cook could step down after the series in India, or after the Ashes tour of Australia in 2017-18.
Speaking on BBC Radio 5 live's Tuffers and Vaughan Cricket Show, he said: "These next six or seven weeks are not crucial for Cook.
"He is breaking records and he has four or five years left as a batsman, if his mind wants to play that long.
"I do get the sense that he will get to the stage, whether it's the end of India or the Ashes in a year's time, where he will say, 'I like the idea of standing at first slip and batting for a few more years.'"
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England seamer Stuart Broad will play his 100th Test in Rajkot, becoming only the 14th England player to do so.
"To play 100 Test matches in any position is a great achievement," said Cook.
"To do it as a seamer in particular is probably a better achievement than a batter because of the physical demands."
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Broad, 30, has claimed 360 Test wickets at an average of 28 since making his debut in 2007.
Only team-mate James Anderson, who will miss the first Test as he continues his recovery from a shoulder injury, and Sir Ian Botham have taken more for England.
"He's turned himself into a fine, fine bowler, one of England's great cricketers," said Cook.
"I've been very privileged to play with some great cricketers for England and he's certainly right up there."
India captain Virat Kohli boasts a career Test average of 45, but only 20 in nine matches against England.
He managed only 134 runs in 10 innings on India's 2014 tour of England, after which he has averaged almost 55.
"I can put it very simply as that was the phase when I didn't perform too well. It happened to be England and could have been any other country in the world," said the 28-year-old.
"It made me realise what I need to improve in my game so I am pretty thankful to England for that. I have been a really improved cricketer from then on.
"I just take it as a setback in my career, and not motivate myself in a way that I have to prove people wrong or I have to do something special against a particular opposition."
Teenage opener Haseeb Hameed will make his England debut against India in the opening Test in Rajkot on Wednesday.