The energetic midfielder leaves for an undisclosed fee thought to be in the region of £4 million.
Behrami joined the Hammers in July 2008 after from SS Lazio and enjoyed a fantastic start to life at the Boleyn, impressing with his work-rate and energy.
A knee ligament injury ruled the Switzerland international out of action for six months in March 2009 and he has struggled to have the same impact on the pitch ever since.
Behrami scored three goals in 63 appearances for the Hammers.