The teams are also scheduled to play three 50-over One-Day Internationals (ODIs) before facing off for two Twenty20 Internationals at the tail-end of the tour, which wraps up on April 6.
Sri Lanka have a good record at home, beating Australia 3-0 in the last series they hosted in August 2016.
But the team will be without some of its star players during the Bangladesh tour following the retirements of Kumar Sangakkara, Mahela Jayawardene, Tillakaratne Dilshan and Muttiah Muralitharan.
Sangakkara, Jayawardene and Dilshan are the only players to have scored more than 1,000 Test runs against Bangladesh while off-spinner Muralitharan claimed 89 wickets in 11 Tests.
"They (Sri Lanka) are going to miss some players who have been part of their team for many days. Regular captain Angelo Mathews is also absent," Rahim said in Dhaka ahead of the team's departure.
Skipper Angelo Mathews was Saturday ruled out of the Tests, even as selectors said they were preparing to field a "formidable team".
The Sri Lankan cricket board did not say why Mathews was dropped, but he returned home last month halfway through the South African tour after twisting his ankle.
Rahim also pointed to his side's bowling variety.
"We have three different types of bowlers in Shakib (Al Hasan), Mustafiz (Mustafizur Rahman) and Miraj (Mehedi Hasan). When they bowl together it would create pressure on any opponent," he said.
Copyright Agence France-Presse, 2017