The Croatia playmaker has made 160 appearances for Spurs, scoring 17 goals, and moves for a fee reported to be ?33million.
The transfer is subject to a medical with Modric due to sign a five-year contract.
"Luka has been a terrific player for us," said Tottenham chairman Daniel Levy, who also revealed the clubs have agreed a new partnership that will see them work together in respect of players, coaches and commercial relationships.
He added: "While we preferred not to part with Luka, we are pleased that it is to Real Madrid, a club with which we now look forward to sharing a long and productive partnership."
Real Madrid president Florentino Perez welcomed the decision for the clubs to work more closely together.
"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,'' he said.
"We are delighted to welcome Luka and look forward to working closely with Tottenham in the coming years.''
The money raised from Modric will fund Spurs' pursuit of Brazilians Willian of Shakhtar Donetsk and Internacional's Leandro Damiao.
