Cresswell was reportedly a target for top-flight rivals West Brom and Fulham but the highly-rated 24-year-old arrives at Upton Park on a five-year deal for an undisclosed fee, despite only signing a new contract with the Championship club in December.
The Englishman is Sam Allardyce's third signing ahead of the new campaign, following the arrivals of Argentinian striker Mauro Zarate and Senegalese midfielder Cheikhou Kouyate as the club attempts to improve on their 13th-place finish last season.
The left-back's transfer is sure to bolster West Ham's defence, having lost out-of-contract duo George McCartney and Jordan Spence.
The former Tranmere Rovers defender - where he spent three years before joining Ipswich in 2011 - was a mainstay in Mick McCarthy's defence last season, appearing 44 times in the league as they finished in ninth position and four points adrift of sixth spot.
