"Niko was a player at Bayern. He is very familiar with the people involved as well as the structure and the DNA of the club," said Bayern's sporting director Hasan Salihamidzic. "We are convinced that he is the right coach for the future of Bayern."
Kovac will bring his 44-year-old brother, Robert, from Frankfurt as assistant coach.
Born in Berlin to Croatian parents, both brothers played for the Croatia national team as well as Bayern.
The elder Kovac was also coach of the Croatian team with his brother as assistant manager.
During a two-year playing stint with Bayern between 2001 and 2003, Kovac won the Intercontinental Cup as well as the 2003 Bundesliga title and 2003 German Cup.
Bayern have been hunting a replacement for Heynckes, who came out of retirement when Carlo Ancelotti was sacked in October after a series of poor results.
Since his return Heynckes has steered Bayern to a sixth consecutive Bundesliga title as well as the semi-finals of the German Cup and the Uefa Champions League where they will face Bayer Leverkusen and Real Madrid respectively.