Keane's move to Liverpool concludes a long transfer wrangle with Spurs
Liverpool have completed the signing of striker Robbie Keane from Tottenham for a fee that could rise to £20.3m.
Keane, 28, underwent a medical on Monday after agreeing personal terms on a four-year contract worth around £80,000 a week over the weekend.
Spurs said they agreed an initial fee of £19m plus a potential further £1.3m.
Tottenham have also agreed to drop their official complaint to the Premier League after Liverpool apologised for their conduct in pursuing the Irishman.
I don't regard it as a transfer deal - that is something which happens between two clubs when they agree to trade
Tottenham chairman Daniel Levy
Relations between Spurs and Liverpool became strained after Tottenham chairman Daniel Levy accused the Reds of breaking Premier League rules in making their interest in Keane known despite being told by the Londoners he was not for sale.
However, a statement on the Spurs website read: "Liverpool FC have acknowledged that the way its website reported comments of its manager, which were widely covered by the media, was inappropriate.
"In light of that acknowledgement (they) have apologised and agreed to make a donation to our Club's main charity, the Tottenham Hotspur Foundation.
"Tottenham Hotspur has therefore agreed not to pursue its official complaint to the Premier League."
But Levy added: "I was incredibly disappointed when I first heard, not only that Liverpool had been working behind the scenes to bring Robbie to Anfield, but that Robbie himself wanted to go and submitted a transfer request to this effect.
"I have already made my opinion clear on the nature of this transaction.
"I don't regard it as a transfer deal - that is something which happens between two clubs when they both agree to trade - this is very much an enforced sale, for which we have agreed a sum of £19m as compensation plus a potential further £1.3m in additional compensation."
Liverpool will now become Keane's sixth club after spells at Wolves, Coventry, Inter Milan and Leeds, before his switch to Tottenham in 2002 for £7m.
Keane had become Benitez's number one summer target over recent weeks, with the need to replace Peter Crouch, who joined Portsmouth earlier this month, seemingly more important than pursuing the protracted move for Aston Villa's 27-year-old midfielder Gareth Barry.
Keane paid tribute to Levy and Spurs and revealed that the move to Anfield was too good to turn down.
He said: "I would like to place on record my thanks to the board, players and fans of Tottenham for the past six years, which were the best and most enjoyable of my career to date.
"I will never forget them. I would specifically like to thank chairman Daniel Levy for understanding, that, as a fan, joining Liverpool is a lifelong dream of mine and one I couldn't let pass me by.
"I hope one day the Spurs fans, who have been brilliant to me, can understand this too.
"I have only good things to say about my time at Tottenham and expect them to go from strength to strength under Juande Ramos and Daniel Levy."
The arrival of Keane takes Liverpool's spending to about £32m since the end of last season. They have already drafted in Philipp Degen, fellow full-back Andrea Dossena, goalkeeper Diego Cavalieri and teenagers David Ngog and Emmanuel Mendy.
About £20m has been raised by selling Crouch, John Arne Riise, Scott Carson and Danny Guthrie.
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