Bundesliga champions Bayern revealed on Friday that Kovac will take charge at the end of the season, when the short-term reign of Jupp Heynckes comes to an end.
Bayern Munich came from behind to thrash Borussia Monchengladbach in their first Bundesliga game since wrapping up a sixth consecutive title.
Kovac will also bring his 44-year-old brother Robert Kovac from Frankfurt as assistant coach. "We acted very professionally because we took advantage of a loophole in Niko Kovac's contract - which he had inserted himself".
Head coach Jupp Heynckes had promised that Bayern would be fully focused despite having wrapped up the 2017-2018 championship last weekend, and his team lived up to those expectations at Allianz Arena after conceding an early goal on a Josip Drmic strike in the ninth minute. He joins from Eintracht Frankfurt, where he had a contract to 2019, for a reported transfer fee of US$2.5 million (RM9.7 million).
Both clubs last week denied Kovac was on his way to Munich.
The Frankfurt coach said his move would have "no influence" on the team's remaining games of the season.
Several high-profile coaches, including Tottenham boss Mauricio Pochettino, were linked with the Bayern job after Heynckes reportedly rejected the offer of a contract extension.
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However. Bayern sporting director Hasan Salihamidzic confirmed the following day that an agreement has been made.
A Bundesliga and DFB Cup double victor with Bayern as a midfielder in 2003, Kovac was Croatia manager as recently as 2015 before taking up the reins at the Commerzbank-Arena.
"We view Fredi Bobic's statement as rather outrageous", Hoeness said. "Not of Eintracht Frankfurt".
"Thomas Tuchel told us that he's signed with another club". "They did their thing and thought of themselves".
The decision, however, in favour of Kovac marks a turn for success-driven Bayern, who had previously opted for big-name coaches including Champions League winners Heynckes, Louis van Gaal and Pep Guardiola.
Kovac is a reactive coach who has started with no fewer than seven different formations in his 30 Bundesliga games this term - something that should appeal to Bayern given the sheer breadth and depth of abilities in their squad; but the Berlin-born former Croatia worldwide still has certain predilections. Champions League qualification is possible this season after another stellar campaign.
In German media, Kovac is regarded to be only second choice for Bayern.