The Croatian midfielder, who is set to move for an undisclosed fee - believed to be around £33m (Dh191.7m) - is due to have a medical today ahead of completing the transfer.
The move comes as the sides agree a new partnership agreement, and will see Modric signing a five-year deal at the Bernabeu.
"Luka has been a terrific player for us," said Daniel Levy, the Tottenham chairman, on the club's website.
"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."
Tony Pulis, the Stoke manager, confirmed the English Premier League side expect to sign US international Maurice Edu from Glasgow Rangers today, with Tom Huddlestone also expected to join on loan.
But Dawson is also on Stoke's transfer target list and Pulis admits he is keep to sign the White Hart Lane club captain.
"I'd love to take Dawson off Spurs but whether we could afford him or not I'm not sure," he said.
"Huddlestone and Dawson and people like that would improve us and make us a better team. If we have to bite the bullet a little bit we have to bite the bullet, but hopefully it will make this club better in future years."
Sunderland have also been linked with a move for the 28-year-old defender, who has slipped down the pecking order at Tottenham and could move before the transfer window closes.
The Brazilian playmaker has been the focus of much interest from the Rossoneri over the summer, but Madrid are keen to ship the player out on a transfer rather than a loan.
And with the transfer window set to close on Friday night, Adriano Galliani, the Italian side's vice-president, says they are not interested in a permanent deal for the 30-year-old.
"They only want to sell Kaka permanently whereas we want him on loan," he told Sky Sports Italia.
"If they change their minds I'm ready to fly to Madrid, otherwise nothing will happen.
"We have five central midfielders and five wingers and I would say we're totally covered."
Tottenham, Manchester City and Newcastle United could all move for French international star Loic Remy before the transfer window shuts. Read our full story here.
Controversial QPR midfielder Joey Barton says he wants to move to French side Marseille.
The 29-year-old - currently serving a 12-match ban following his red card on the final day of last season against Manchester City - has been linked with a move to the Ligue 1 giants before the end of the transfer window.
And with the player unlikely to feature for QPR again following his behaviour - which saw him stripped of the captaincy - he announced on Twitter his heart was 'already in the Velodrome'.
"I want to leave," he said. "I hope to move on with my career, with my life. If that is in France, so be it.
"I don't want to be disrespectful to QPR but enough is enough."
Czech midfielder Petr Jiracek is set to join Hamburg from Bundesliga rivals Wolfsburg.
The Euro 2012 player only joined Wolfsburg during the last transfer window from Victoria Pizen, but now Felix Magath, the Wolfsburg manager, is ready to let the 26 year old move on.
"Hamburg want him and we are in a situation where we can do without him," he said.
"And now the player wants to go to Hamburg too."
Argentina international defender Fabian Monzon has joined Lyon from Nice in a swap deal for forward Jeremy Pied.
The deal values Monzon, capped seven times by Argentina, at EU3m (Dh13.8m), though that fee could rise to EU4m depending on bonuses.
The 25-year-old - who scored eight goals in 34 appearances for Nice - will likely replace Aly Cissokho, who is expected to join Valencia later this week in a EU6m deal.