Keane completed his sensational return to White Hart Lane after six months at Liverpool, the 28-year-old agreeing a four-year deal, with the fee starting at £12m before rising with add-ons.
It meant there was no significant outlay for Spurs to re-sign the striker due to the money still owed by Liverpool.
Keane, following Defoe and Pascal Chimbonda as players rejoining Spurs, left for Anfield in the summer but has paid the price for failing to fit into the plans of boss Rafael Benitez.
The Republic of Ireland striker travelled to London yesterday to agree personal terms and complete a medical.
"It was a difficult decision to make to leave Tottenham in the summer," Keane said. "It proved not to be the right move for me.
"I know some Spurs fans will feel I let them down by leaving but I can assure them I shall be giving my all for this club - this club has terrific fans and I want to repay them for all their support. We've got to get on and fight our way up that league table."
Spurs boss Redknapp had stated his admiration for Keane, setting the wheels in motion for one of the most dramatic and swift returns.
Liverpool were unhappy with Redknapp's comments, while Spurs chairman Daniel Levy had been upset by Keane demanding a transfer last summer - but a deal was pushed through to get the Republic of Ireland captain back.
Levy added: "We never wanted Robbie to leave in the summer, we acknowledged the six years dedicated service he gave this club and reluctantly let him go.
"I am delighted that he has chosen to return to us. We can all recall the passion and fight he displayed during his previous seasons with us. I know he is determined to give us his full commitment."
Keane's debut is expected to be this weekend in the derby against neighbours Arsenal, although he is cup-tied for the Carling Cup final against Manchester United next month.
Fellow striker Defoe, however, will endure more Wembley misery after being ruled out for up to 10 weeks with a stress fracture to his right foot.
The 26-year-old England international, who missed two trophy victories last season, will undergo surgery to repair the problem, meaning he will miss the Carling Cup final.
"Following further scans and examination, Jermain Defoe will undergo surgery after suffering a stress fracture in his right foot,'' read a statement from Spurs.
"Early detection has allowed the club to opt for the best long-term treatment."
Defoe picked up the injury, to his fifth metatarsal, during an indoor training session shortly after rejoining Spurs after almost a year at Portsmouth.
During that time, the former West Ham striker missed out on Spurs' Carling Cup victory as he had just moved to Fratton Park, and then missed Pompey's FA Cup win as he was cup-tied.