Off contract in June, the Germany international had been courting interest from across Europe.
Arsenal, Liverpool, Manchester City and Barcelona were all interested in Kimmich, who is free to discuss pre-contract terms with any foreign club.
Indeed, the player stated earlier this week that "many clubs" were being mentioned as a potential destination for himself.
However, Sky Deutschland's Florian Plettenberg is reporting Kimmich and Bayern have now reached terms over a new deal.
He said on X: "BREAKING | Total verbal agreement between FC Bayern and Joshua #Kimmich on a new contract until 2029!
"Green light from the entire Bayern board. Final paperwork is in progress. Contracts are set to be signed this week, with the announcement planned soon."
Kimmich's decision is a great endorsement for coach Vincent Kompany, who has Bayern well placed in the Bundesliga and Champions League in his first season in charge.