The former Ipswich Town full-back has signed a five-year deal at Upton Park and becomes the club's third signing of the summer, joining Cheikhou Kouyate and Mauro Zarate
The 24-year-old has signed a five-year contract at Upton Park, with the two clubs agreeing an undisclosed fee.
In his final season at Portman Road, Cresswell made 42 appearances - scoring two goals and providing 14 assists - and was voted into the Championship Team of the Year by his peers at the end of the season.
Cresswell becomes Sam Allardyce's third signing of the summer, following the arrivals of midfielder Cheikhou Kouyate and striker Mauro Zarate.
Allardyce has been tasked with bringing an entertaining style to Upton Park this season along with a top-10 finish.