The left-back's arrival completed the first part of an expected double swoop by Jose Mourinho's side on the Spanish giant, with Gareth Bale also sealing a sensational return to the club.
Reguilon starred on loan with Sevilla last season, helping the club to UEFA Europa League success and a fourth-place finish in LaLiga.
His form earned Reguilon a first senior cap for Spain earlier this month amid reported interest from Manchester United, Chelsea and Paris Saint-Germain.
However, Tottenham has won the race for the 23-year-old's signature, while Madrid is thought to have inserted a buy-back clause into the deal.
Sevilla was also in the running to sign Reguilon but accepted defeat in its pursuit earlier this week, instead bringing in Marcos Acuna from Sporting CP.