Keane watched Liverpool's win over Chelsea from the stands on Sunday
Tottenham have re-signed striker Robbie Keane from Liverpool, six months after he left the club for an initial £19m.
Keane has signed a four-year contract at Spurs with the fee starting at £12m and rising with add-ons.
"It was a difficult decision to make to leave Tottenham in the summer," the 28-year-old told the club website.
"It proved not to be the right move for me. I know some Spurs fans will feel I let them down... but I can assure them I'll be giving my all."
He added: "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."
I don't think he got a great crack of the whip there but that's up to Rafa Benitez
Tottenham manager Harry Redknapp
Keane joined Liverpool from Spurs in July in a deal which could have risen to £20.3m but failed to establish himself in manager Rafael Benitez's first-team.
The Republic of Ireland captain managed only five goals in 19 appearances for the club he supported as a boy.
Spurs manager Harry Redknapp told BBC Radio 5 Live that Keane was never given a fair chance at Anfield.
"I don't think he got a great crack of the whip there but that's up to Rafa Benitez, he picks the team and he obviously didn't see Robbie as a player who fitted into his system or a player that he particularly wanted," said Redknapp.
"He had a great time at Tottenham and I never thought he would be a player who would leave White Hart Lane. Liverpool came in, as he said he was a Liverpool supporter as a kid and it was a great opportunity to play Champions League football. It hasn't worked out for him, we all make mistakes in life.
Keane was on the losing side at White Hart Lane on 1 November
Tottenham chairman Daniel 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 made 254 appearances for Spurs during his first spell between August 2002 and July 2008, during which time he scored 107 goals.
He becomes the third player manager Harry Redknapp has brought back to White Hart Lane this month, following fellow striker Jermain Defoe's return from Portsmouth and defender Pascal Chimbonda's transfer from Sunderland.
"I'm very pleased to have signed him, he's just the type of player we need - his enthusiasm, his work rate, he's a terrific character to have around the place," Redknapp added.
"He's going to be very important in the dressing room because he's a leader and that enthusiasm and will to win will be great for us."
Redknapp, meanwhile, confirmed he spoke to Inter Milan boss Jose Mourinho regarding a move for Ricardo Quaresma and that Mourinho had given his approval, only for Chelsea to enter the race and sign the winger on loan until the end of the season.
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