The 30-year-old striker signed for the Hammers from Hull City on a two-year contract, with the option of a further two, and is excited to again compete in the Premier League under former Croatia boss Bilic.
He told whufc.com: "I am very excited to be signing for West Ham United, especially as it is a big Club and I didn't know until a couple of days ago that I would have the opportunity to come here.
"Of course it is always a target to play in the Premier League, so when I found out that West Ham wanted me there was no doubt that I wanted to come here.
"I've played for Slaven before for the Croatia national team and he is a great manager and a great man. I am really happy and delighted to be working with him and all his staff again.
"I'll be joining a team that's on a high after the result on Saturday."