The Welshman, who will be presented as a Real player on Monday, has finally secured a move to the Bernabeu after weeks of intense speculation and Tottenham manager Andre Vilas-Boas has wished the 24-year-old well.
"We wish him all the best, he's left us with great memories from last season, which I think every Tottenham fan cherishes," Villas-Boas said.
"But he has moved on and we move on as well."
Bale, who scored 26 goals in 44 appearances for Spurs last season, secured a clean sweep of awards - taking the Professional Footballers' Association Player of the Year and Young Player of the Year, as well as the Football Writers' Association Player of the Year gong.
Despite his heroics, Tottenham could not secure a spot in the UEFA Champions League, finishing fifth behind rivals Arsenal, sparking doubt over Bale's future at White Hart Lane.
Bale's switch to the Spanish capital had been expected for some time, with an option to purchase Bale's shirt prematurely appearing on Madrid's website only making the deal more inevitable.
A number of Real players, including Fabio Coentrao, Angel Di Maria and Alvaro Morata had been mooted as potential makeweights in the deal, but none have been included in the deal.
Carlo Ancelotti has been busy reshaping his squad since replacing Jose Mourinho in the close-season, bringing Casemiro, Dani Carvajal, Asier Illarramendi and Isco to the club for a reported combined fee in the region of €75m.
Spurs boss Villas-Boas has already gone some way to replacing Bale in his squad, signing the likes of Roberto Soldado, Erik Lamela, Nacer Chadli and Christian Eriksen to boost the club's attacking options.
NEWSBale thanks Tottenham
NEWSAVB wishes Bale success
NEWSLevy sad to see Bale leave
Tottenham Hotspur hold talks for player who could REPLACE Dominic Solanke: report
'William Saliba isn't in the three best centre-backs in the league - I like him, but at the moment, Gabriel is performing better than him and I would love Saliba to get more goals': former Arsenal captain issues challenge to defender
