"Joe's going to join Tampa Bay and it might happen pretty quickly if he can get international clearance, etc," Coventry boss Tony Mowbray told the Coventry Telegraph, adding that the out-of-contract midfielder would have been offered fresh terms had he opted to stay in England.
"I would have liked to have kept Joe, who I think has proven his fitness and worth to the team. He's a fantastic character around our building -- no airs and graces, not looking for favours or extra days off," Mowbray added.
"I think Joe can help us control football matches but he's made his decision for his family, and we wish him well because he's been fantastic for our dressing room and this football club."
Cole began his career at West Ham United before moving to Chelsea in 2003. He made 183 appearances for the Blues, winning the Premier League and the FA Cup three times.
News that makes sense
Your trusted source for staying up-to-date with the world around you. Get free daily news updates and analysis, straight to your inbox.
The midfielder also earned 56 caps and scored 10 goals for England.
Cole returned to West Ham in 2013 after a move to Liverpool and a loan spell at French Ligue 1 side Lille.
He was released by the Hammers in 2014 and moved to Aston Villa, for whom he made 16 appearances in total, before joining Coventry.
(Reporting by Simon Jennings in Bengaluru; Editing by John O'Brien)
