The 25-year-old midfielder, who can play on the left and centrally, joins after leaving League One side Plymouth Argyle by mutual consent earlier today.
Cooper’s move follows the arrival of attacker Michal Gyasi.
“I’m very excited for the season coming,” Cooper said after signing. “I’ve not had the best last couple of years so I’m excited to get going in pre-season.
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“I want to get a lot of games under my belt and get the club back to where it should be. I spoke to the manager a few times and he’s just got to get the best out of me.
“This is perfect for me right now to be here with the manager and with the club.”
Cooper has had a tough couple of years with two knee injuries, making just three appearances in all competitions last season.
Earlier this year Pilgrims boss Steven Schumacher said that he could leave despite having a year remaining on his contract, stating a fresh start was needed for the Warrington-born man.
Cooper came through the academy at Crewe, making more than 140 appearances and scoring 15 goals, which led to Peterborough United paying a fee for him in January 2018.
After joining Plymouth on loan, he played a big part in helping them win promotion from League Two in the 2019/20 season, assisting an impressive 12 goals from left wing-back.
His form persuaded the Pilgrims to turn his loan into a permanent deal, signing a three-year contract.
He departs the Greens after making 51 appearances in total, scoring five goals.
Cooper follows Branden Horton, Bailey Clements, Ryheem Sheckleford, Joe Cook, Darren Oldaker and Michael Gyasi in penning deals with the Spireites this summer.