The midfielder has signed a three-year deal with Hull after a fee was agreed with the Hammers on transfer deadline day.
He will head out on international duty with Senegal before joining up the Hull squad, but is already looking forward to the start of a new challenge.
“I’m very excited to be here and I have been waiting for this moment to sign,” Diame told the club's official website.
“Speaking to the owners, the manager and everybody at the club, I am very happy to be here.
“I want to thank the manager and the owners for showing belief in me and now I will make sure I repay that faith on the pitch.
“I have to go away to play for Senegal, but I am looking forward to returning here next week to get started.
“It’s a new challenge for me and one that I am looking forward to. I want to play football and Hull City do it very well.
“I know that after playing against this team last season. Even in the game when they had ten men, they played really well.
“I’m just looking forward to getting started.”
Diame has happy memories of the KC Stadium after scoring his first goals in English football in 2011 with Wigan Athletic when they won 3-2 against Hull.
“I do remember that,” added Diame. “But now I hope to score for Hull City at the KC Stadium.”