Heynckes came out of retirement in October 2017 to take temporary charge of the side in the wake of Carlo Ancelotti's dismissal, but rebuffed Bayern's attempts to get him to stay beyond the end of the season, bundesliga.com reported.
The club's search for a replacement came to an end on Friday when it was announced that Kovac, who played for the Bavarians for two years between 2001 and 2003, will take over in time for the 2018/19 campaign.
"He's hard-working, innovative, eloquent, and lives for football," Heynckes said when asked about Kovac's impending arrival on Friday. "He's a good man-manager too. I believe Bayern has made a great decision bringing him in.
"He works with many different types of player with varying nationalities in Frankfurt, and he's doing a wonderful job. He's predestined to coach Bayern. He's a good choice. It'll work out."
There were mixed feelings for Kovac himself, however. "I said a week ago that I'd had no contact with Bayern. That all changed yesterday when I received a telephone call and a contract offer from Munich.
"It's not easy, I have to say. It's hard to think that my time here is coming to an end soon. But where one door closes, another opens. My decision will have no effect on our remaining games this season. We'll keep working as hard as we always have. We need to put all our efforts into these final few games."
Kovac will be visiting his home for next season and beyond in two weeks, when Frankfurt travels to face Bayern at the Allianz Arena on Matchday 32.