The Croatia international, who has reportedly cost Madrid €35m (£27.6m), has been heavily linked with a move to the La Liga champions throughout the summer.
Madrid and Tottenham, as well as concluding a deal for Modrić, have also penned a partnership agreement which will see the clubs work closely together in the future.
Real Madrid president Florentino Perez Rodriguez said: “The strong relationship and affinity between our two clubs has resulted in the cementing of a longer-term partnership and the successful transfer of Luka Modrić.
“We are delighted to welcome Luka and look forward to working closely with Tottenham in the coming years.”
Chelsea made two attempts to sign the 26-year-old last summer, but Tottenham chairman Daniel Levy stood firm in his refusal to sell the playmaker to their London rivals.
But Levy, while insisting Spurs did not want to sell their star player, is pleased to have laid down the foundations for a “productive partnership” with the Bernabéu outfit.
“Luka has been a terrific player for us and, whilst we preferred not to part with him, we are pleased that it is to Real Madrid, a club with which we now look forward to sharing a long and productive partnership,” said Levy.
Modrić scored 17 goals in 160 appearances for Spurs after moving from Dinamo Zagreb in a £16.5m deal in 2008.
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