While he was unable to end Spurs' wait for a first English top-flight title since 1961, Levy leaves behind a legacy that includes a new stadium and state-of-the-art training ground as well as a first major trophy since 2008 following their Europa League triumph last season.
"I didn't expect it, didn't see that coming," Kane told British media ahead of England's World Cup qualifier in Serbia on Tuesday.
"Daniel has been a fantastic chairman for Tottenham in the 20 years or so he's been there.
"Considering where the club was and where it is now, I think it's been a big change, not just on the pitch, but off the pitch as well," added Kane, who joined Bayern Munich in August 2023.
"Overall for Tottenham, it's a new chapter they're trying to create now."
Speculation about a possible change of ownership has increased since Levy stepped down, though the club's majority shareholder has said Spurs are not for sale.
While Spurs chief executive Vinai Venkatesham described Levy's contribution as "extraordinary" he downplayed the potential for upheaval following his departure.
"The club is well organised for succession, so we have a very strong executive team in place and, whilst it might feel like a slightly strange thing to say to the external world, although it's big news, inside the club, it really is business as usual," he told the club's website on Monday.