He is set to be joined at Tottenham by Real team-mate Sergio Reguilon.
Spain left-back Reguilon flew with Bale to London after a £27million fee was agreed between the two clubs.
Tottenham boss Jose Mourinho was asked about the possibility of signing Bale earlier this week.
But the Portuguese was coy on any rumours.
“Gareth Bale is a Real Madrid player and I don’t comment on players from other clubs,” he said.