The selectors, who met in Chennai, once again overlooked middle-order batsman Yuvraj Singh and retained youngster Cheteshwar Pujara, who made his debut against Australia in Bangalore earlier this month.
Gambhir and Sharma were nursing knee injuries that kept them out of the Bangalore Test while Laxman missed the match because of a back problem.
Opener Murali Vijay, who replaced Gambhir in Bangalore, has been retained in the 15-member squad led by Mahendra Singh Dhoni, secretary of the Indian cricket board N Srinivasan said in a statement on Monday.
Ahmedabad hosts the first Test from (Nov. 4-8), while Hyderabad (Nov. 12-16) and Nagpur (Nov. 20-24) are the venues for the two other matches.
Mahendra Singh Dhoni (captain), Virender Sehwag, Gautam Gambhir, Murali Vijay, Rahul Dravid, Sachin Tendulkar, Vangipurappu Laxman, Suresh Raina, Cheteshwar Pujara, Harbhajan Singh, Zaheer Khan, Ishant Sharma, Shanthakumaran Sreesanth, Pragyan Ojha, Amit Mishra.
Meanwhile, the Rajasthan Royals say they have filed a petition in the Bombay High Court against the national cricket board's decision to expel the team from the Indian Premier League.
The Board of Control for Cricket in India removed the Royals earlier this month following charges that it had broken shareholding and ownership rules. King's XI Punjab was also ousted on similar charges.
The Royals say in a statement they have been trying to meet with the BCCI discuss the matter and “do not understand what we have done wrong.” They also say the case is expected to be heard on Wednesday.
Elsewhere, Paceman Peter Siddle and wicketkeeper Brad Haddin have returned to Australia's squad for next weekend's Twenty20 match with Sri Lanka in Perth after injury, selectors said Monday.
Siddle is available for Sunday's game after a lengthy rehabilitation from a back injury, while Haddin has returned to full fitness following an elbow complaint.
Haddin's return meant there was no place available for Tasmanian wicketkeeper Tim Paine, who played in the Test and one-day series in India this month.
"It’s exciting to see the return of Peter Siddle and Brad Haddin into international cricket," chairman of selectors Andrew Hilditch said.
"Peter is a key bowler in all forms of the game and has made a return from injury and is now ready to take his place in the Australia Twenty20 squad.
