The returning duo has been out of the team for several months with Chandimal's last international appearance coming during his side's humiliating whitewash at the hands of Australia.
Mathews could not feature in Sri Lanka's historic Test series win in South Africa earlier this year due to a hamstring issue but he represented his team throughout the World Cup and was named Player of the Series in the three ODIs versus Bangladesh.
Dananjaya returns to the Test side after remodeling his bowling action, which was deemed suspect by the ICC in November last year.
The players left out from the preliminary squad include Kasun Rajitha, Asitha Fernando, Danushka Gunathilaka, Shehan Jayasuriya, Chamika Karunaratne, Dilruwan Perera and Angelo Perera.
Following Chandika Hathurusingha's sacking, Rumesh Ratnayake will serve as the interim head coach for Sri Lanka.
The first Test begins on August 14 at Galle while the next game will start on August 22 in Colombo. The results of both matches will count towards the calculation of points in the World Test Championship.
Dimuth Karunaratne (c), Angelo Mathews, Dinesh Chandimal, Lahiru Thirimanne, Kusal Mendis, Kusal Perera, Niroshan Dickwella, Dhananjaya de Silva, Akila Dananjaya, Lasith Embuldeniya, Suranga Lakmal, Lahiru Kumara, Oshada Fernando, Lakshan Sandakan, Vishwa Fernando