Sources told ESPN Spurs paid €30 million for the defender after agreeing to Madrid's demand for a buyback clause to be included in the deal.
Reguilon, 23, is a Madrid youth product who excelled on loan at Sevilla last season, becoming an important part of a team that won the Europa League and finished fourth in La Liga.
Los Blancos coach Zinedine Zidane preferred Marcelo and Ferland Mendy as his left-back options, but senior figures at the Bernabeu insisted that the club retain the option to bring Reguilon back if he continues to progress.
Reguilon's impact at Sevilla -- after first breaking into the Real Madrid team in 2018-19, picked by then-coach Santi Solari ahead of Marcelo -- caught the eye of a number of top European clubs.
United and Inter Milan were both keen, and Sevilla would have liked to keep him for another season but were unable to compete financially.
Sources told ESPN that Reguilon preferred a new challenge in the Premier League and was open to joining United before Spurs agreed terms with Madrid.
He was then convinced by the personal interest Spurs manager Jose Mourinho had taken in his signing, while the relationship between Florentino Perez and Daniel Levy also helped secure an agreement.