Redknapp: Spurs have got one over Gunners
Gallas, 33, rejected the offer of a new contract with Arsene Wenger's team earlier this year before signing a one-year deal on reduced terms at White Hart Lane, ending his four-year association with the Gunners.
And Redknapp insists his squad have laid down the red carpet treatment for Gallas, as the ex-Chelsea centre-back looks to build up his fitness on the training ground ahead of making his debut for Spurs after the international break in a fortnight.
Speaking to the London Evening Standard ahead of Wednesday's Champions League second-leg qualifier with Young Boys Berne, Redknapp said: "I don't think the players are concerned about William's Arsenal connection.
"This time last year, Patrick Vieira wanted to come to Tottenham. Patrick was a legend at Arsenal but I spoke to him and he was very keen to come and play for Tottenham.
"They are professional footballers. William's career took him to Chelsea and Arsenal but he is here and part of us now. He belongs to Tottenham. I think it shows you the courage these boys have got.
"They could take the easy way out and go and play abroad somewhere but he is willing to take the flak. He knows he is going to get some flak from the Arsenal fans but his signing is one-up for us. Tottenham fans should be thinking, 'Hang on, we have got one over on them here'.
"He is willing to come to Tottenham and play. He is a good player and a great asset to us. On a free transfer, he is a great bit of business."
Redknapp also moved to quash speculation linking him with moves for Luis Fabiano, Lassana Diarra and Steven Pienaar before the transfer window shuts next week.
He said: "I would be surprised if there is anything happening here before the window closes. It could, but at the moment I couldn't say we are close to doing any deals, selling or buying. It is pretty dead out there."
By James Martini