According to The Sun, the Croatian midfielder had already said he would join Jose Mourinho's side, but was waiting for both clubs to reach a deal.
He almost ruined his chances of a move by refusing to go on Spurs' pre-season tour, but Real officials persuaded him to apologise and return.
The Spanish giants were initially reluctant to meet Spurs' valuation but Mourinho wanted Modric as soon as possible.
The deal will bring an end to a saga, which began when the 26-year-old demanded a move to Chelsea a year ago.
Spurs refused to comment on the matter, but accepted he would move on this summer, the report said. (ANI )