Spurs had been sweating on clearance to bring the 27-year-old to White Hart Lane after technical difficulties hampered their efforts to submit the relevant paperwork for the move before transfer deadline.
But after investigating the club's claims that there were difficulties involving computer servers between themselves and Real, the Premier League ratified the £8 million signing.
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."
Tottenham announced: "We are delighted to announce that we have reached agreement with Real Madrid for the transfer of Rafael van der Vaart."
Manager Harry Redknapp on Tuesday night revealed he was alerted to Van der Vaart's availability just two hours before the window closed.
Redknapp also claimed the player had been set to join Bayern Munich for £18million on Monday but the move broke down.
However, that was categorically denied on Wednesday afternoon by the Spanish giants, with sports director Miguel Pardeza telling his club's official website, www.realmadrid.com: "It is absolutely false that Real Madrid received a 21million euro offer from Bayern Munich for Van der Vaart.
"In fact, the German team never showed an interest to sign the player, so the allegations made in England have greatly surprised us."
Source: PA
Source: PA