Real did not reveal the fee but Spanish media reports said they have agreed to pay Chelsea $114 million for the Belgium international, who was set to become a free agent in June 2020.
Reyes, who shot to fame at Sevilla before a switch to Arsenal followed by spells at Real and Atletico Madrid, was on the books with second tier Spanish club Extremadura.
Real Madrid favourite Zinedine Zidane returned for a second spell as coach on Monday with plans to rebuild the Spanish giants who have fallen into crisis since he left in May after winning an unprecedented third straight Champions League.
Barcelona handed Real Madrid another demoralizing loss, beating its arch rival at Santiago Bernabeu Stadium for the second time in a week and taking full control of the Spanish league.
Despite splashing hundreds of millions on new players since taking over in 2011, PSG's Qatari owners have not been able to buy success in the competition they crave the most with four successive quarter-final exits between 2013 and 2016.
Jose Mourinho, former Manchester United manager, accepts one-year prison sentence but he will not serve any jail time after swapping the sentence for a fine of close to $2.2 million.
Real Madrid lift the FIFA trophy for a record fourth time after thrashing local side in Abu Dhabi with the help of impressive distance strikes in either half from midfielders Luka Modric and Marcos Llorente.
The UEFA Champions League round of 16 will see three England-Germany clashes and a true test of the Premier League v Bundesliga.
Real Madrid's Croatia midfielder Luka Modric has been named Best FIFA Men's Player of the Year for 2018, while Orlando Pride's Brazil forward Marta won the women's award.
Real Madrid were playing their first competitive game since all-time top scorer Cristiano Ronaldo left and Julen Lopetegui succeeded Zinedine Zidane as coach.
Real Madrid won the epic clash 3-1 against Liverpool to claim their fourth Champions League title in five years, with Gareth Bale scoring twice.
The Spanish giants are targeting their fourth Champions League title in five years and their third in a row in the game. Liverpool will be hunting their first trophy in 11 years.
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