Hitzlsperger said: "The manager who signed me at Lazio got sacked after a week and the new manager didn't fancy me.
"That happens sometimes. It was frustrating but you just have to get on with it. I have always wanted to come back to the Premier League.
"I had a really good time when I was in England and I knew this is where I wanted to be. I want to prove myself and play week in and week out."
Hitzlsperger admits he could have joined other teams in Europe but feels West Ham can challenge in the top half of the table.