The 24-year-old joins the club on a five-year contract for an undisclosed fee.
Cresswell immediately flew out to join his new team-mates on their pre-season trip in the south of France.
“I’m very excited to have signed here,” told Cresswell. “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.
“It’s been a pretty hectic couple of days, but we got there in the end. I signed late on the Thursday night, so I didn’t get back to Ipswich until late on.
“The team flew out on Friday morning and I arrived at lunchtime on Saturday. The boys trained in the morning and now I’ll be joining them in the gym for their second session of the day.”