He will join Hull in a deal that is worth £1.5 million. His time at the Hammers included many loan spells at clubs like Bradford, Wigan and Bolton.
And since he was not seen as a member of the first team squad by new manager Manuel Pellegrini, the time was right for a permanent departure.
Burke is an academy product.
Writing on Twitter, Burke said: "I achieved my dream of playing in the Premier League for my boyhood club and scoring a winner in front of the home fans, that is a moment I will never ever forget.
"But I feel right now is the time I need to move on as a player to further my career.
"The club will always have a special place in my heart and I would like to thank everyone at West Ham and all of the fans that have supported me at my time at this amazing club."