The France defender has moved from Chelsea for a fee believed to be around £25million.
The France centre-half, 26, has agreed a four-year contract after joining for an undisclosed fee, believed to be around £25million.
“I’m very happy and very proud,” Zouma told West Ham TV.
“My conversation with the manager went very fast. I just felt like he really wanted me to come and join the team, especially a good team that’s started the season very, very well.
“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 may be top of the early-season table but they have conceded five goals in their three matches so far after Saturday’s 2-2 draw with Crystal Palace.
Moyes was also desperate to add to his squad with the added burden of a Europa League campaign this season.
Moyes said: “I am delighted to welcome Kurt to West Ham United. He 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 am very happy that he is now our player.
“Kurt will join a squad full of players who are hungry and ambitious. He will provide competition to our squad. He is a strong, powerful player with great experience in the Premier League while he is also at a good age for a centre-back.
“Kurt has enjoyed great success at Chelsea and I can see that he is determined to continue being successful here at the London Stadium.”