The 44-year-old former Peterborough boss has been in charge of first-team affairs since Kevin MacDonald departed the club on July 12.
Cooper, previously assistant to MacDonald, has overseen two wins and two defeats from his four matches in charge of the Robins.
"I'm really pleased with opportunity," Cooper told the club's official website. "Obviously it's an exciting project and I'm delighted to be part of it. I hope to be involved in the long-term future of the club."
The club's board of directors revealed that Cooper's work during his interim period in charge of the SkyBet League One side persuaded them to chose him over other candidates.
Chairman Jed McCrory said: "The manner in which Mark Cooper has conducted himself as caretaker manager after Kevin's departure left the board with little alternative but to offer him the job.
"His work-rate and commitment to the club has been phenomenal. We considered several candidates - all well qualified - but kept reverting back to Mark.
"He has grown enormously over the last few months and, with the respect he commands from the players, the board feel that Mark is capable of leading the club into a what we hope will be a hugely successful season."