Redknapp said: "This is a good deal for the club.
"It's a big signing, a big transfer fee for this club but if you look around the Premier League, you see this sort of money being spent almost every week. I think we've got real good value. The price is good for a player of that quality.
"I don't think the club has spent a lot of money. Under Mark (Hughes) players came in on free transfers and were paid decent wages but I don't think you'll find the club has spent a lot on transfers."
Remy had met with Newcastle chiefs before his U-turn but Redknapp said he believed his history with the player, as well as assurances over his role in the side, were deciding factors.
"I spent four hours with him last season when we were looking to take him at Tottenham," the former White Hart Lane boss added. "We got on great so I thought we had a head start. He wanted to come to London.
"I said to him that I wanted him to play through the middle, whereas I think he felt he might have been playing in a wide position had he gone elsewhere."