The pair are scheduled to fly in a private jet after completing medicals in Madrid.
Bale is set to re-join Spurs on a season-long loan deal, and he's expected to continue to earn his £600,000-a-week salary. Both Spurs and Real Madrid will contribute to his pay for the 2020-21 season.
Bale's agent, Jonathan Barnett, said Thursday that he thinks the pact will be completed this week.
Before earning a transfer to Real Madrid worth £85.3 million, the Welsh attacker established himself as one of the world's top players during his spell at Spurs from 2007 to 2013.
Meanwhile, Reguilon - who was previously linked with Manchester United - is leaving Real Madrid to join Spurs on a deal worth €30 million. The Spanish left-back has already agreed to a long-term contract.