That is the only change to the squad that was named for the second Test against South Africa, which was drawn earlier this week.
Pradeep, who helped Sri Lanka earn a 1-0 series win in England earlier this year, adds fast bowling cover to a squad which also includes Shaminda Eranga, Suranga Lakmal, Dhammika Prasad and Chanaka Welagedara.
Both Eranga and Lakmal face fitness tests ahead of the opening match.
The opening Test takes place in Galle before the Sinhalese Sports Club in Colombo hosts Mahela Jayawardene's final Test match starting on 14th August.
Sri Lanka Test squad: Angelo Mathews (captain), Lahiru Thirimanne (vice-captain), Niroshan Dickwella, Shaminda Eranga (fitness permitting), Rangana Herath, Mahela Jayawardene, Suranga Lakmal (fitness permitting), Dilruwan Perera, Nuwan Pradeep, Dhammika Prasad, Kumar Sangakkara, Kaushal Silva, Upul Tharanga, Kithruwan Vithanage, Chanaka Welagedara
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