The Croatia playmaker has joined Real Madrid for a fee reported to be around £33million and is due to sign a five-year contract with the Spanish side.
As part of the deal, Spurs and Real Madrid have agreed to a new partnership that will see them work closer together.
"Luka has been a terrific player for us," said Tottenham chairman Daniel Levy.
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."
"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," Real Madrid president Florentino Perez said.
"We are delighted to welcome Luka and look forward to working closely with Tottenham in the coming years."