Redknapp expects to complete the free transfer signing once the 33-year-old French defender, who agreed a one-year contract with an option to extend the deal, has passed a medical on Friday.
Gallas was left looking for new employers after Arsenal baulked at his high wage demands, reportedly 80,000 pounds a week, and opted to release the former Chelsea star.
But the wage issue has not put off Spurs boss Redknapp, who said: "He's a no-brainer on a free transfer.
"He's never asked for big money here. The chairman's agreed a one-year contract with him and the wages are more than reasonable."
But Redknapp had already shrugged off any controversy there could be from Gallas crossing the north London divide.
"He's been an Arsenal player but he was at Chelsea before that and playing abroad before he arrived there," he said recently.
"It's not like we would be signing Tony Adams. He's a good player and he would be a very useful addition to our squad."
With Jonathan Woodgate still out with a long-term groin injury and captain Ledley King plagued by knee problems that have the potential to limit his playing time, Redknapp has been keen to bolster his defensive resources.
Gallas will be Spurs' second signing since the end of last season, following that of Sandro.
The Brazilian midfielder's arrival in the UK is imminent after he helped Internacional win the Copa Libertadores.
Source: AFP European Edition