Redknapp is unworried by the defender's connections to Arsenal or Chelsea. Gallas spent four years at the Gunners after spending five years at Stamford Bridge before that.
"It's all cobblers," Redknapp said ahead of the completed deal. "What's he done? It's not the Yorkshire Ripper I'm signing, is it? He's a footballer, he plays football.
"He's not the first player to go from Arsenal to Tottenham or Tottenham to Arsenal. It happens all the time. He's a great lad as well, smashing fellow.
"I've been absolutely really impressed with him. He'll improve Tottenham and that's all I'm concerned about."
OTHERS WHO HAVE CROSSED THE NORTH LONDON DIVIDE
Jimmy Robertson (Spurs 1964-48/Arsenal 1968-70): The only player to score for both teams in the derby
Steve Walford (Spurs 1975-77/Arsenal 1977-81): Just two Tottenham appearances before Gunners boss Terry Neill took him to Highbury
Pat Jennings (Spurs 1964-77/Arsenal 1977-85): The legendary Northern Irish goalkeeper won the FA Cup with either club (1967 and 1979)
Sol Campbell (Spurs 1992-2001/Arsenal 2001-06): Suffered years of vitriol and abuse from the Spurs faithful over his switch to Arsenal, where he won two league titles and three FA Cups
Arsenal boss Arsene Wenger gave Gallas his best wishes on the move across north London, and intimated his exit was somewhat inevitable following the summer arrival of centre-back Laurent Koscielny from Lorient.
"I can completely understand that," said Wenger. "At the moment he's looking for a club, he's free. He has chosen the best possible option for him.
"We are thankful for what he has done for us and we wish him good luck in his new club."
And asked if Gallas could come back to haunt his old club, the Frenchman added: "There is just a little bit of a risk that he is a bit more exposed in the derby, but we have seen that before."
With Jonathan Woodgate still out with a long-term groin injury and captain Ledley King plagued by knee problems that limit his playing time, Redknapp has been keen to bolster his defensive resources.
Gallas, who will also provide competition to centre-backs Michael Dawson, Sebastien Bassong and Younes Kaboul, was not registered for European competition so he will be unable to play against Young Boys in the second leg of Spurs' Champions League qualifier on Wednesday.
Wenger 'surprised' by Gallas decision
Redknapp admitted that the acquisition of Gallas may not mark the end of his summer spending, with Brazilian Sandro being Tottenham's only other capture of this transfer window.
The 21-year-old defensive midfielder will arrive at the club next week after helping Internacional to the Copa Libertadores title against Mexico's Chivas Gudalajara.
A £7m deal for Sandro was agreed back in March but the player - who has been learning English since then - was allowed to stay with Internacional for as long as the club were in the Copa Libertadores.
"It was the farewell of my dreams," he said after lifting the trophy on Wednesday. "I dreamed of being champion and leaving with this trophy in my luggage."
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