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 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.
