Tymoshchuk, 29, is expected to arrive at Bayern at the start of July, Hoeness said.
No financial details of the contract were revealed but German media reports put the deal at 14 million euros ($17.89 million).
"It is my understanding that we will have the player in Munich by July 1," Hoeness told reporters, adding he could come earlier depending on the Russian championship season and the domestic transfer rules.
"We have agreed with the player but not yet with Zenit on the date. There are still some question marks regarding whether he will come in April or July."
Bayern have already signed for next season striker Ivica Olic from Hamburg and talented Borussia Monechengladbach player Alexander Baumjohann.
Hoeness said he also hoped to keep captain Mark van Bommel, 31, for another season after offering him a one-year contract extension.
Van Bommel's contract is running out at the end of this season and he has not yet said what he intends to do.
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