The 27-year-old has been a regular in the Hammers midfield since his arrival on a free transfer from Wigan Athletic in June 2012.
Diame made 33 appearances and scored 3 goals in his first season for the Hammers. He followed that up with 4 goals from 35 league appearances last season.
With Diame only having 10 months remaining on his original three-year contract, the club decided to accept an undisclosed offer from Hull City.
Diame’s departure comes as no surprise following the recent arrivals of Cheikhou Kouyate and Alex Song.