Bale, 31, left Spurs for a then world record £85m in 2013 and has scored more than 100 goals for Real in a spell where he has won four Champions Leagues.
He has also won two La Liga titles, the Copa del Ray, two Uefa Super Cups and three Club World Cups but he has been allowed to leave after seven years at the Santiago Bernabeu.
While he didn’t win any silverware during his time with Spurs, he was twice crowned PFA Player of the Year during his six years at White Hart Lane after arriving from Southampton in 2007.
Despite enjoying plenty of success in Spain, Bale has endured a difficult relationship with Real manager Zinedine Zidane and was close to sealing a move to Chinese side Jiangsu Suning a year ago.
The Wales captain made just 12 starts in La Liga last season, scoring twice and providing two assists.
The club confirmed that he will take the number 9 shirt, his fourth different number at Spurs, while Reguilon will wear number 3.
‘It’s nice to be back,’ said Bale. ‘It’s such a special club to me, it’s where I made my name.
‘What an amazing club, amazing fans, it’s incredible to be back.
‘Hopefully now I can get some match fitness, get underway, help the team and hopefully win some trophies.’
Reguilon has also joined from Real Madrid, with Spurs beating Manchester United to his signature.
The 23-year-old Spanish right-back impressed on loan with Sevilla and will link up with Bale in a Tottenham Hotspur shirt next season after signing a five-year deal.
More to follow…