Left-arm spinner Lakshan Sandakan and paceman Dushmantha Chameera have been dropped from the squad, which beat Zimbabwe in the one-off Test in Colombo earlier this month.
Yet to earn his Test cap, the 30-year-old Pushpakumara has for long been prolific at the first-class level, picking 558 wickets at an average of 19.85.
While the first Test will be played at Galle, the second game will be played in Colombo from August 3-7 followed by the third and final at Pallekele from August 12-16.
Squad: Rangana Herath (Captain), Upul Tharanga, Dimuth Karunaratne, Kusal Mendis, Angelo Mathews, Asela Gunaratne, Niroshan Dickwella (WK), Dhananjaya de Silva, Danushka Gunathilaka, Dilruwan Perera, Suranga Lakmal, Lahiru Kumara, Vishwa Fernando, Malinda Pushpakumara, Nuwan Pradeep.
