Modric will wear the No. 19 shirt with Real Madrid and said he has "no hard feelings" with Tottenham after completing his move.
Modric, who refused to travel with his former teammates for Spurs' pre-season tour of United States and forced his move to Real, said: "There are no hard feelings. I want to thank everyone there. I spent three great years there and enjoyed every moment."
The Croatian completed his move to Real Madrid in a deal totally worth £33 million.
The Londoners will receive £27m from La Liga champions while the rest £6m will be paid in various add-ons. The transfer saga finally ends as Spurs were not ready to budge on their £40m valuation.
The move will help both clubs develop business in respect of players, coaches and commercial interests. But the transfer of Modric is a big blow to Spurs chairman Daniel Levy who expected to bag £35m plus from the sale of Modric. In 2010, Dutchman Rafael van der Vaart made his move from Real to Tottenham in a deal worth £8 million.
"Real Madrid and Tottenham Hotspur have reached an agreement for the transfer of the player Luka Modric, who will remain attached to the club for the next five seasons. Both clubs have also formalised an agreement of collaboration," Real confirmed on their official website.
However, Spurs are now expected to make huge signings after cashing in on Modric's high-profile transfer. Manager Andre Villas-Boas is desperate to bring in players after securing only 1 point in opening two games of the new campaign.
Spurs are planning to spend nearly £50m on hot targets Willian from Shakhtar Donetsk and Leandro Damiao of Internacional. However, Ukrainian club Shakhtar rejected a £11.8m bid for the Brazilian. The 20m-rated star was also target for Manchester United.
Tottenham defender Michael Dawson was linked with a £9m move to London rivals Queens Park Rangers but the 29-year-old centre-half rejected the offer and is not reluctant to leave White Hart Lane. Meanwhile, Sunderland and Stoke City are planning to bid for Dawson.
France midfielder Yann M'Vila and Loic Remy were linked with a move to the Premier League with Tottenham's North London rivals Arsenal also interested. Spurs were also interested in French goalkeeper Hugo Lloris but talks stalled after the players asking price.
Spurs are eyeing many high-profile moves but have £50m to spend if they want to acquire their targets.