The board brought back all-rounders Dasun Shanaka and Dhananjaya de Silva to the squad led by Dinesh Chandimal.
Former skipper and all-rounder Angelo Mathews has recovered from a recurring calf injury and was included in the squad.
During Sri Lanka's home series against India, the hosts lost all nine games -- three Tests, five one-day internationals and a lone Twenty20 -- between July and September.
After playing the first Test in Kolkata from November 16-20, the teams move to Nagpur for the second, which starts on November 24. The final Test will be played in Delhi between December 2-6.
Squad: Dinesh Chandimal, Dimuth Karunaratne, Dhananjaya de Silva, Sadeera Samarawickrama, Angelo Mathews, Lahiru Thirimanne, Rangana Herath, Suranga Lakmal, Dilruwan Perera, Lahiru Gamage, Lakshan Sandakan, Vishwa Fernando, Dasun Shanaka, Niroshan Dickwella and Roshen Silva.