The veteran midfielder has fond memories of his time at the treble winners, but will return to Russia after four years in Germany
The Ukrainian midfielder had an expiring contract with the Bundesliga giants and eventually decided not to extend his stay at the Allianz Arena, but return to his former club instead after four years at Bayern.
"It was very hard to say farewell, but it's always been like that, whenever I've left a previous club. It's always a difficult decision when you choose to move on, and it affects the family too, especially when you're playing with such a good team like here in Munich, at an amazing level and with such great success," the midfielder told the official Bayern website.
"We all get on very well with each other, and I'll certainly stay in touch with a number of the players. I've had four superb years.
"There have been so many good moments. I've had four outstanding years here, with many moments I'll never forget. The first championship in 2010, and the treble this season were outstanding, only seven teams have ever managed that."
The 34-year-old previously wore the Zenit jersey from 2007 until 2009.