He will still remain as director, though former director and ex-managing director of Waitrose, David Felwick, will return to the club as chairman.
Brent's majority shares in the club have been bought by American Simon Hallett.
In a statement, Brent remarked: "It has been an incredible privilege to lead Argyle's board as custodians of our club over the last seven years. It's now time for the next exciting chapter to begin.
"I'd like to thank Simon and [his wife] Jane for their considerable financial commitment, which unlocks huge opportunities for the club and wider community."
Hallett also responded: "I'd like to thank James Brent for all his hard work and excellent leadership.
"Plymouth Argyle is a club I am passionate about and believe can deliver much success in the future. This investment puts the club in a strong position to continue to move forward.
"I am delighted for the board to appoint a chairman of David Felwick's calibre. I look forward to seeing the next stage of the club's development."