The 26-year-old made headlines in October when he explained he was not willing to receive his first dose due to what he perceived as a lack of research into possible long-term effects.
Kimmich has not featured for Bayern since 7 November after twice being forced to isolate due to being a close contact of someone who tested positive for coronavirus.
In an interview with ZDF to be broadcast in full later on Sunday, Kimmich revealed he is now in a position where he feels ready to get vaccinated.
"Generally, it was just difficult for me to deal with my fears and concerns, which is why I was undecided for so long," Kimmich said.
Despite being absent for the past month, Kimmich has featured 18 times for Bayern across all competitions this campaign.
Bayern, which is playing its home games behind closed doors due to coronavirus restrictions imposed in Bavaria, beat Mainz 2-1 on Sunday in Kimmich's absence.
Julian Nagelsmann's men are now six points clear at the top of Bundesliga and face Stuttgart on Tuesday in their penultimate game of the year.