Off-spinner Sunil Narine and all-rounder Kieron Pollard, who have not played international cricket since November 2015, were included in the 14-man squad for the series against Australia and South Africa starting from June 3.
Brathwaite and Marlon Samuels, who played key roles in West Indies' World T20 triumph earlier this year, have also been included but the squad does not include all-rounder Andre Russell, Sammy, Bravo and Gayle, all involved in Indian Premier League cricket.
The day/night series starts in at the Guyana National Stadium from June 3-7 and then moves to Warner Park, St Kitts (June 11-15) before concluding at Kensington Oval, Barbados (June 19-26).
West Indies squad: Jason Holder (capt), Sulieman Benn, Carlos Brathwaite, Darren Bravo, Jonathan Carter, Johnson Charles, Andre Fletcher, Shannon Gabriel, Sunil Narine, Ashley Nurse, Kieron Pollard, Denesh Ramdin, Marlon Samuels, Jerome Taylor.