The former Oldham Athletic and Mansfield Town man is now set for a move to the USA.
Black, 25, joined the Robins on a one year deal last summer. He made a total of four starts and one substitute appearance for the club.
"I would like to thanks everybody at Cheltenham Town for their support since I have been at the club," Black said.
"It's a fantastic club, great people and a great place to live. On a personal note, I just want to play football and my opportunities have been limited so after discussions with the manager, this was a decision which was best for both parties.
"I hope the team can turn things around and finish the season strongly. There is a good group of young players who will keep improving and I am sure the team will go on to be successful.
"Thanks again and best of luck to everyone associated with Cheltenham Town."
Everyone at Cheltenham Town would like to wish Paul every success for the future.