Atapattu, 35, had been out of action since March due to a chronic back problem which required surgery in Australia in May. He missed the tour of England and the ongoing Test series against South Africa.
Mahela Jayawardene, who replaced Atapattu as captain for the England tour, will continue to lead the side with the former skipper confined to his role as a specialist batsman, a Sri Lanka Cricket release said on Saturday.
Atapattu has scored 8,233 runs in 253 One-dayers at an average of 37.7 with 11 centuries.
Sri Lanka go into the August 14-29 tri-series buoyant by a 5-0 rout of England earlier in the summer.
Each team plays the other twice in the league with the top two teams advancing to the final on August 29.
India, led by Rahul Dravid, are due to arrive here on August 10.
Sri Lanka's one-day squad:
Mahela Jayawardene (capt), Kumar Sangakkara, Sanath Jayasuriya, Upul Tharanga, Tillekeratne Dilshan, Marvan Atapattu, Chamara Kapugedera, Prasanna Jayawardene, Farveez Maharoof, Chaminda Vaas, Muttiah Muralitharan, Dilhara Fernando, Lasith Malinga, Malinga Bandara, Ruchira Perera.
Coach: Tom Moody