The 24-year-old left Town this summer to sign a five-year deal with the Hammers.
He told the Tractor Boys' official website: "It's great to have the chance to come back to Ipswich and properly say my goodbyes to the players, the staff and the supporters.
"Ipswich put faith in me and I want to put on record my sincere thanks to the owner, Mick McCarthy and Paul Jewell - who signed me - and the fans at Ipswich for their fantastic support over the past three years."
Cresswell came through the system at Tranmere before moving to Ipswich in 2011, where he would go on to make over 140 appearances.
He added: "It was difficult to leave the club as I'd built up a great relationship with everyone there but like any player I want to play in the Premier League and joining a fantastic club like West Ham is a great opportunity for me.
"I genuinely wish Ipswich every success for the season ahead and I'll be keeping an eye on their results."