"We have reached an agreement with the St Petersburg side, with the president [Alexander Dyukov] and trainer Dick Advocaat," Karl-Heinz Rummenigge told the paper.
Ukrainian international Tymoshchuk, 29, will "play for Zenit until June 15, and then take a two or three-week break before coming to us," Rummenigge said.
Tymoshchuk is expected to sign a contract to keep him at the club until 2012. Sport Bild said that Bayern would pay the Russians 11 million euros ($13.8 million).
The midfielder signed for Zenit in February 2007 for around $20 million, which at the time made him the most expensive player in Russia.
He was instrumental in taking Zenit to their first Russian title in his debut season and played a major part in the club's triumphant 2007/08 UEFA Cup campaign.
Zenit face Stuttgart in St. Petersburg in the first-leg of their UEFA Cup Round of 32 tie on Wednesday evening.