Nicknamed 'The Hammer' due to his powerful left foot, Hitzlsperger should find favour among the West Ham fans, and Sullivan expects great things from the former Bayern Munich youth player.
"Thomas is a top-quality player who I know the fans will love - and not just because of his nickname," Hammers chief David Sullivan said.
"He is a wholehearted midfielder with an eye for a goal who gives everything in every match."
Hitzlsperger has previous experience of the Barclays Premier League having spent several seasons at Aston Villa between 2000 and 2005.
Hitzlsperger began his career at Bayern before joining Villa at the age of 18. He made his debut for the club in 2001 and went on to make 114 appearances for the midlands outfit, scoring 12 goals.
He returned to Germany with Stuttgart in summer 2005 and went on to lift the Bundesliga title with the club two years later. He joined Lazio in January this year but only made five appearances before his short-term deal expired.
Hitzlsperger has won over 50 caps for the German national side but missed out on a place in Joachim Low's World Cup squad this summer.
Sullivan also said: "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."