McCarthy had previously tried to sign the 21-year-old when he was manager of Wolverhampton Wanderers.
"They were big factors in me coming here. Mick was interested in me when I was at West Ham and I worked with Terry Connor for a while after joining Wolves in the summer. They are two people who have a lot of respect in the game," he told the club's official website.
"I know it's going to be a battle to get in the side. One look around the squad tells me that but you need that competition to be successful. I'm relishing the challenge and can't wait to get going here."
Nouble has been handed the number 35 shirt at Portman Road.