Newcastle boss Kevin Keegan had an £18.5million bid rejected by the Croatian club yesterday afternoon before Spurs upped the ante to land the star.
A top Dinamo source said: "Everything has been agreed and Modric will be going to Tottenham. All the details are in place and the fee is £20m."
Modric will sign a five-year deal with Tottenham. The deal is believed to be a club record fee for Spurs whose previous record was the £16.5 signing of Darren Bent from Charlton last summer.