Gayle, who is West Indies' most successful batsman in the T20 format with 1519 runs at an average of 35.32, replaced Lendl Simmons, who had struggled for runs in the T20 series against Afghanistan.
It will be Gayle's first T20 match at his home ground, Sabina Park. The marauding batsman, who has two T20 centuries, last played an international match for the West Indies in the 2016 World T20 final against England at Eden Gardens.
All-rounder Jason Holder, who leads the side in Tests and ODIs, has been rested again and the side will be led by Carlos Brathwaite.
"He will get the chance to play on his home ground and against a top-quality Indian team," Browne added.
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The hosts are trailing 1-2 in a five-match ODI series with India and will strive to equal the rubber by winning the final match tomorrow.
West Indies T20 squad:
Carlos Brathwaite (C), Samuel Badree, Ronsford Beaton, Chris Gayle, Evin Lewis, Jason Mohammed, Sunil Narine, Kieron Pollard, Rovman Powell, Marlon Samuels, Jerome Taylor, Chadwick Walton and Kesrick Williams.