'Weight off my shoulders': Bayern's Kane toasts breakthrough title
Champions heading into the game, Bayern beat Borussia Moenchengladbach 2-0 at home, with Kane scoring the opener with a header after 31 minutes, his 25th league goal of the season.
Drenched with beer after being chased and doused by teammates on the Allianz Arena pitch, Kane told Sky Germany the trophy was "a long time coming".
"It's cold, but there's going to be a few more today for sure," a soaked Kane told reporters.
The 31-year-old had lost six finals in his career -- three with former club Tottenham, two with England and one with Bayern -- as well as a second-placed league finish with Spurs.
The England captain finally tasted team success last Sunday, when chasers Bayer Leverkusen drew 2-2 at Freiburg.
Kane said: "It was a weight on the shoulders so it was nice to have that lifted -- and now we can enjoy it."
The striker added the title win was "an incredible feeling... it's worth the wait".
"It's been a lot of hard work, a lot of sacrifice in between, for moments like this -- to enjoy it with the team, enjoy it with the fans. I'm loving every minute," he said.
"We're going to enjoy this for sure, but then hopefully this is just the first of many.
"We have a great team, a great coach and yeah, we feel like we're building, so we're looking forward to the challenge."
Kane also praised long-time England teammate Eric Dier, who will leave Bayern in the summer. The title win was also Dier's first of his career.
With Spurs through to the Europa League final where they will face Manchester United, Kane wished his former club well, two years after leaving boyhood club Tottenham.
"It's been a tough season but to reach the Europa League final is a great achievement," Kane said.
"It's no easy feat to beat the teams that they've beat, so full credit to them.
"I'll be watching and hoping they can win, and it could be a good month for a lot of Spurs fans, because I know a lot of them have reached out to me and they're happy to see me lift this title.
"And of course I think we'd all be happy to see Spurs win that in a couple of weeks."