The Hammers are thought to have accepted a £3.5m deal which triggered his buy out clause. Diame, 27, joined the Hammers from Wigan two years ago on a free transfer.
Diamé made his debut for West Ham on August 2012 in a 1–0 win against Aston Villa. He scored his first goal for the Hammers in the 3–1 defeat to Arsenal in October 2012. His second goal for the club was scored in the 3–1 victory over Chelsea in December 2012.
He made 79 appearances in all competitions in a West Ham shirt scoring seven goals.
Hull City Manager Steve Bruce said: “I’m delighted to welcome Mo to the Club. His experience, both at international level and in the premier league will be invaluable as we look to cement our place in the top-flight.”