Sullivan insists the 28-year-old is the first of many signings to come at Upton Park this summer.
Hitzlsperger has become new manager Avram Grant’s first signing at the club.
“I am delighted to welcome Thomas to the club,” Sullivan told the club’s official website.
“We had to move quickly to secure his services when he became available, especially as there was understandably so much interest in him from around Europe and back in Germany.
“I am especially pleased that he is excited by what we are trying to achieve here at West Ham.
“Thomas is a top-quality player who I know the fans will love – and not just because of his nickname. He is a whole-hearted midfielder with an eye for a goal who gives everything in every match.
“He is the first of many signings this summer.
“We are going to sign a mixture of exciting young talent as well as the very best senior pros who can add real strength to the squad like Thomas. He is still a young man, but has massive experience.”