The 14-member squad also includes Andre Russell, subject to him passing a fitness assessment prior to the series.
"We felt that players like Narine and Pollard, who have played well in T20 leagues around the World, once they are fit and mentally ready to play, we must give them the opportunity to represent the West Indies again," said interim chairman of the CWI Selection Panel, Robert Haynes while announcing the squad on Tuesday.
Narine last played in a T20I for West Indies against England almost two years ago at Chester-le-Street and batting all-rounder Pollard appeared last November on India tour.
Wicketkeeper-batsman Anthony Bramble, who has played 12 T20 games and 46 List A games, has earned a maiden call-up to the side that also includes Khary Pierre and John Campbell in the squad which will be led by Carlos Brathwaite.
Veteran opener Chris Gayle made himself unavailable for the series and will feature in Canada's Global T20 League instead.
After the first two T20Is in Florida on August 3 and 4, the final match of the series will be played in Guyana on August 6 before the three-match ODI series and two Tests.