The 24-year-old was a free agent after being released by the Sky Blues at the end of last season.
The newest addition to Cook’s squad made 73 appearances for the League One side after joining from Preston in 2012, and has made one senior appearance for Northern Ireland.
Talking to the club’s official website, Barton said: “This is a massive club and the manager was also a big factor in why I wanted to come here.
“He’s won this league before and the way I like to play is the same way that he likes to play, so that’s another positive.
“I like to get the ball down and play it forward – I’m always disappointed if I give it away.
“The fans were another big reason why I wanted to join the club. Coming to a place like this gives you such a boost.”