The 20-year-old, who spent time on loan with Sheffield United and Notts County last season before being released from Old Trafford, has agreed a one-year contract.
He told the club's website: "Obviously I'm happy to be here. I've been here for 10 days training and they're a great bunch of lads. It's great being here so far.
"I spoke to the gaffer here and the plans he's got for the club here, I want to be a part of.
"I'm going to get my head down, work hard and when I get the opportunity I'll show what I can do."
Boss David Flitcroft feels Ghana-born Cofie is one for the future.
He said: "I saw him when he was at Burnley as a kid. He's a player of immense potential and immense talent.
"I don't think he'll be ready for the start of the season. There's bags of potential there.
"Once we'd evaluated him over the week's training, the decision to sign him was easy."