The Premier League have officially ratified the deal after their investigation into whether the full details of the transfer were made before the deadline.
Technical problems on the London club's computer servers prevented the £8 million transfer going through before the 6pm deadline on August 31, but Spurs have now secured the signature of the 27-year-old midfielder.
The Premier League said in a statement: "The Premier League can confirm the transfer of Rafael van der Vaart's registration from Real Madrid to Tottenham Hotspur."
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Tottenham announced: "We are delighted to announce that we have reached agreement with Real Madrid for the transfer of Rafael van der Vaart."
The Netherlands international came through the ranks at Ajax and won two league titles during 141 appearances with the Eredivisie side, scoring 60 goals before leaving for Hamburg in the summer of 2005.
Van der Vaart has been capped by Holland a total of 83 times, scoring 16 goals, since making his international debut against Andorra in 2001 at the age of 18.
The midfielder is quoted in the Dutch media as saying: "The interest from Tottenham came very quick and I did not have much time to think.
"But I want to play football again and if possible every week, with a beautiful club. I'm totally happy.
"I am excited about playing in England. Whether it suits my style remains to be seen, but I think a good footballer can adapt and I am very proud of this transfer."
He added: "It's a pity I cannot now play against Ajax in the Champions League but I will get to face FC Twente."
Spurs boss Harry Redknapp revealed he was alerted to Van der Vaart's availability just two hours before the window closed by chairman Daniel Levy.
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