The 23-year-old signed agreed an 18-month loan at the Veltins Arena last month after making seven substitute Bundesliga appearances for Bayern this term following his close-season arrival from Mainz.
Kirchhoff admitted he had become frustrated at a lack of first-team football under Pep Guardiola, and a loan move to Schalke represented a perfect opportunity to remedy that feeling.
The Gelsenkirchen outfit sit seventh in the German top flight after a solid first half of the season, and Kirchhoff is confident he can help them maintain their form.
"The situation in Munich was not easy for me," he told Schalke's official website.
"I learned a lot in half a year, but just did not play too much.
"I had reached a point where I said that I was no longer satisfied.
"I am very happy that the transfer worked. I am very grateful, and look forward to a new challenge at a great club."
Kirchhoff's first league game for his new club could come on January 26 when they return to Bundesliga action against Hamburg.
Get the best features, fun and footballing frolics straight to your inbox every week.
Thank you for signing up to Four Four Two. You will receive a verification email shortly.
There was a problem. Please refresh the page and try again.