The midfielder has left Liverpool on a permanent transfer, signing a two-and-a-half-year deal with the club where he first got his footballing breakthrough. The deal is believed to be a free transfer, although there have been suggestions that Liverpool have handed him a payoff to allow the move to go through.
Cole moved to Liverpool on a free transfer after becoming marginalised at Chelsea, but injuries and poor form ensured that he made just 9 starts for the club, with 26 appearances in total bringing 3 goals.
The player will now be hoping to finally get some regular football under his belt as he works with new manager Sam Allardyce. West Ham, meanwhile, will be hoping that he can help the club climb back up the table and avoid getting caught in a relegation battle.