Kane, 30, will now decide whether to leave Spurs or see out the final year of his contract in north London.
Bayern had threatened to walk away from negotiations after setting a deadline of midnight last Friday for Spurs chairman Daniel Levy to respond to their latest bid.
Levy waited until Monday to reject that proposal but Bayern returned with one final offer which is thought to have been restructured with amended add-ons and a higher proportion of the fee guaranteed up front.
Spurs have now accepted that offer, not least because Kane has shown no willingness to sign an extension to his £200,000-a-week deal, which expires in 2024.
The England captain has scored 213 Premier League goals and is on course to surpass Alan Shearer's record of 260. Kane is also motivated by a desire to win silverware, having never lifted a trophy for club or country despite establishing himself as one of the world's top strikers.
Sources have told ESPN that Kane has enjoyed the positive brand of football new coach Ange Postecoglou is attempting to implement at Spurs and took a full part in preseason, including scoring four in last weekend's 5-1 win over Shakhtar Donetsk.
However, the lure of joining Bayern to elevate his career is obvious given they have won the Bundesliga title in 11 consecutive seasons and the last of their six Champions League triumphs came in 2020 -- when thrashing Spurs 7-2 during the group stage.
Kane wanted his future resolved by the start of the Premier League season -- Spurs face Brentford in their opening match on Sunday -- and must now determine whether his future lies in England or Germany.
Reports in Germany suggested that Kane's wife, Katie Goodland, had been spotted last month in Munich looking at houses, fuelling speculation over a potential move.
However, Spurs' reluctance to let the player leave placed the possibility of a deal in doubt before a breakthrough came on Wednesday.