Litton has sufficiently recovered from a calf injury and will join a 16-man group that will depart for Bangladesh's first Test tour to Australia in 23 years.
The 31-year-old missed the recent all-format tour to Zimbabwe but was man-of-the-match in the last Test he played against Pakistan in Sylhet in June, scoring 126 and 69 in a 72-run victory.
"The 31-year-old batsman has been sidelined since June due to the injury, but has responded well to his rehabilitation programme and will be in consideration for selection for the opening Test," the BCB said on Saturday. "He will fly to Darwin on Sunday to join the squad."
Bangladesh have hit hard by injuries, especially in the bowling department, ahead of the trip Down Under with pacemen Nahid Rana and Shoriful Islam ruled out.
The Tigers will play a three-day warm-up game against a Cricket Australia XI in Darwin from 6 August before the first Test begins on 13 August.
The second and final Test pf the series begins in Mackay on 22 August.
Bangladesh Test squad: Najmul Hossain Shanto (capt), Soumya Sarkar, Shadman Islam, Tanzid Hasan, Mominul Haque, Mushfiqur Rahim, Amite Hasan, Jaker Ali, Mehidy Hasan Miraz (vc), Taijul Islam, Taskin Ahmed, Hasan Mahmud, Khaled Ahmed, Ebadot Hossain, Musfik Hasan, Litton Das
Bangladesh head coach Phil Simmons admits his team "let ourselves down" after collapsing to 54 all out and a defeat in a three-day practice match ahead of the Test series against Australia.
Australia top-order batter Marnus Labuschagne is well rested ahead of bumper 18 months of Test cricket.
Litton Das Has been appointed as Bangladesh's new ODI captain, replacing Mehidy Hasan Miraz, the country's cricket board president Tamim Iqbal has confirmed.
Bangladesh chief selector Habibul Bashar admits "there was a bit of desperation" after recalling Soumya Sarkar for the Test series in Australia, despite a five-year absence in the longest format.
