The 33-year-old Frenchman, twice a Premier League title winner with Chelsea before joining Arsenal in 2006, has agreed a one-year deal with Tottenham and was due to complete a medical later on Friday.
GEAR:Get 10% off your new Tottenham shirt with Gallas printed on the back
If he joins Spurs as expected Gallas would become the first player ever to play league football for London's three biggest clubs, Spurs, Arsenal and Chelsea.
He is a free agent after failing to agree a new contract with Tottenham's bitter north London rivals Arsenal. Redknapp said the Frenchman, who has played 84 times for France scoring five goals, had taken a considerable drop in salary to move to White Hart Lane.
"He is having his medical later and all being well he'll be a Spurs player today," Redknapp told reporters at Tottenham's training ground in Essex.
"I just think it's a no brainer - a player of that experience and that quality on a free transfer. He's a top class defender and I'm well pleased to have him here."
EYEBROWS RAISED
Gallas's connections with Chelsea and more importantly Arsenal have raised eyebrows but Redknapp played down any negative reaction from Tottenham fans who never forgave Sol Campbell for running down his contract with the club before joining Arsenal.
"He's not the first player to go from Arsenal to Tottenham or Tottenham to Arsenal," Redknapp said. "It happens. (Carlos) Tevez went from Man United to Man City. He is a footballer and a great lad and I've been very impressed with him.
"He will improve Tottenham and that's all I'm bothered about. He's shown character to want to come and play here. He's got the bottle to come and want to play here. He's done nothing wrong."
Gallas's temperament has occasionally been questioned.
He once sulkily sat down on the pitch during an away game at Birmingham and lost the Arsenal captaincy after that incident in 2008 following an interview in which he questioned the courage of some of his team mates.
"I don't think his attitude can be questioned, he gets annoyed with people who are not as professional as he is which is not a bad thing, that can't do any harm," Redknapp said.
"Whenever we've played against him I've thought he was a world class defender."
Tottenham's official club historian Andy Porter told Reuters he would be the first player ever to appear for Spurs, Arsenal and Chelsea.
"There has yet to be a player to feature for all three clubs in either the Football League or Premier League," he said.
Clive Allen played for Chelsea and Spurs and also signed for Arsenal but never played for them. George Graham playe
Ella Toone: Why isn't the midfielder playing for Manchester United and England?
'David Beckham was desperate to play in my squad, but I didn't want to bring him along and waste the FA’s money: I had to pick the strongest players': Great Britain coach reflects on Becks snub as 'one of the toughest decisions' of his career
