Burke was at Bolton for the first part of the season, where he made 15 impressive appearances. They were eager to re-sign the player, and the deal has now been completed.
The move is a bit unusual, as Burke featured in three games for West Ham in January – all in the FA Cup. But he is now on loan, and will only get a chance at his parent club next season.
Burke will be hoping he can do enough to impress manager David Moyes as he makes plans for his squad for the next campaign.