The Hammers confirmed on Thursday that they had secured the services of the left-back on a four-year deal, despite reported interest from West Bromwich Albion.
Speaking for the first time since his switch, the 24-year-old told the club's official website: "I'm very excited to have signed here. It's a massive club and I can't wait to get ready for the season ahead.
"When I knew West Ham were interested it was an easy decision to make. Everyone knows it's a massive club and a couple of years down the line they'll have the new stadium too."
Cresswell has already linked up with his new teammates, who are undergoing some pre-season training sessions in France.