The 26-year-old has been amid a long-running saga between Spurs and the Spanish champions after the playmaker announced his intention to leave White Hart Lane earlier this summer.
It is understood that Spurs chairman Daniel Levy has been in a tussle with Madrid over what he deems to be an appropriate transfer fee but it has been confirmed that Modric will complete his switch to the Bernabeu in the next few days.
Real Madrid president Florentino Perez Rodriguez said on Tottenham's official website: "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 Modric. We are delighted to welcome Luka and look forward to working closely with Tottenham in the coming years."
Levy added: "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."
Reports have claimed that a fee in the region of £33m has been agreed between the two parties.