Redknapp revealed: "I spoke to Avram Grant last week and he told me he was interested in taking Crouch to Chelsea when he was in charge there.
"And I was talking to Sven Goran Eriksson the other day as well. When I told him we were signing Peter he said, â€˜Fantastic. He's a terrific player'.
"I was first interested in signing Crouchie last year but I didn't think I had a chance of getting him back here. But he's the sort of bloke who's not happy when he's not playing and that's when we really got involved.
"As great a club as Liverpool is, he was sitting on the bench every week or only playing a bit-part. And he felt that wasn't what he wanted from his life.
"He could have stayed at Liverpool and seen out his contract. But this isn't a financial move. He just wants to play football."
It is the third time Redknapp has signed Crouch, who has agreed a four-year deal.
Redknapp said: "I was director of football when he first came to Portsmouth in 2001. Milan Mandaric wasn't crazy about signing him, but manager Graham Rix was really pushing for Peter and he proved to be a great buy for us.
"Three years later I signed him for Southampton and within a year he was playing for England.
"He's a much better player now, though. His confidence is sky-high and you can see he really believes in himself."
Crouch added: "I'm not going to stand here and lie about Portsmouth's chances of breaking into the top four.