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 Tuesday's transfer deadline.
But after investigating the club's claims that there were difficulties involving computer servers used in the transaction between themselves and Real, the Premier League ratified the signing of the Holland international.
Van der Vaart is quoted as telling the Dutch media: "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."