It is Campbell's first call-up for limited over cricket. The 25-year-old made his test debut in the just-completed series against England, which West Indies won 2-1.
He scored 176 runs at an average of 35.2.
Brathwaite, who hit Ben Stokes for four consecutive sixes to secure West Indies' victory in the final of the 2016 World Twenty20 against England, has played 28 ODIs and 35 Twenty20 internationals.
Cottrell, a left-arm pace bowler, has appeared in six ODIs and 10 Twenty20 internationals.
The first two matches of the four-match ODI series will be played at Kensington Oval in Barbados on Wednesday and Friday.
(Reporting by Andrew Both in Cary, North Carolina; editing by Amlan Chakraborty)
