The former Mainz star had grown frustrated with his role as a substitute and is keen to prove his worth at his new club after joining Schalke for an 18-month spell
The 23-year-old agreed an 18-month loan at the Veltins Arena after making just seven substitute Bundesliga appearances for Bayern this term following his close-season arrival from Mainz and admits that he had become frustrated at a lack of first-team football under Pep Guardiola.
"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.