The Welshman's big-money move to the Santiago Bernabeu was confirmed on Sunday after the clubs finally agreed a deal for his transfer.
Bale has signed a six-year contract at Madrid and will be officially unveiled on Monday.
Levy conceded that he never wanted to lose the 24-year-old but could not convince him to remain at White Hart Lane.
"Gareth was a player we had absolutely no intention of selling as we look to build for the future," Levy said on the club's official Twitter account.
"He is a player whose career we have fostered and developed and he was only a year into his new four year contract.
"Such has been the attention from Real Madrid and so great is Gareth's desire to join them, that we have taken the view that the player will not be sufficiently committed to our campaign in the current season.
"We have, therefore, with great reluctance, agreed to this sale and do so in the knowledge that we have an exceptionally strong squad.
"We wish Gareth all the best in the future and he shall always be welcome at the Lane.”
Bale's performances last season, in which he scored 31 goals for club and country, attracted interest from Madrid and the move has been on the cards for several weeks.
He departs on the same day that Tottenham lost to fierce rivals Arsenal 1-0 in the Premier League.
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