Worcester based Powell, 19, graduated from the Robins' youth team and signed a one-year professional contract last summer.
He spent time on loan at John Brough's Cinderford Town in the Southern League Division One South and West earlier this season.
"We have agreed to let Adam move on and he wants to go down a different avenue in his life, so we wish him all the best," boss Paul Buckle said.
Black, 24, has made four starts and one substitute appearance since joining the Robins from Mansfield Town ahead of the 2014/15 campaign.
"Paul needs to go and get some games and we have good cover in the left-back position with Craig Braham-Barrett and James Bowen," Buckle said.
Cheltenham play Hartlepool United away tomorrow (3pm).