Financial details of the deal were not disclosed but British media reported that West Ham would pay about £25 million ($34.42 million) for the 26-year-old centre back.
With Zouma's transfer complete, it could spell progress toward Chelsea bringing in highly touted defender Jules Kounde from Sevilla FC. Sources had told ESPN's James Olley earlier this week that Chelsea were hopeful of completing a deal worth in the region of €50m for Kounde once Zouma's situation was settled.
Kounde, 22, is keen on a move to Chelsea but Sevilla are believed to be demanding the majority of any transfer fee paid up front. The exact fee and the structure of payments are yet to be formally agreed but sources told ESPN the two clubs are nearing an agreement.
Zouma made 36 appearances for Chelsea in all competitions last season, helping the team win the Champions League title and finish fourth in the Premier League.
"[Zouma] is a player we have tracked for some time, and we have taken great care and diligence to make the transfer happen. He was always our first choice and I'm very happy that he's now our player," West Ham manager David Moyes said in a statement.
"I just felt like he [Moyes] really wanted me to come and join the team, especially a good team that's started the season very, very well," said Zouma.
"With the great season that West Ham had last year, that gave the team a lot of confidence to improve this year -- and I want to help the team do that."
West Ham are currently top of the Premier League table with two wins and a draw from three matches, having been held 2-2 at home by Crystal Palace on Saturday.
Information from Reuters was used to this report.