Bayern's attempts to convince the 72-year-old Heynckes otherwise were unsuccessful.
The 46-year-old Kovac, who played for Bayern from 2001-03, agreed to a three-year contract starting in July, the Bundesliga champions said Friday.
Bobic blasted Bayern on Friday for the timing of its announcement that Frankfurt coach Kovac would be switching to Bayern next season, and for not getting in touch beforehand.
The new manager, born in Berlin to Croatian parents, is under contract to Frankfurt until 2019 and reports in the German media have suggested his release clause is €2.2m (£1.9m).
Rummenigge also defended Bayern, adding: "I have to say that, from our point of view, there are no irritations".
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.
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. But his role at the club could take a positive turn under Kovac next season.
"We view Fredi Bobic's statement as rather outrageous", Hoeness said.
"Thomas Tuchel told us that he's signed with another club". "In this phase which is extremely important for Eintracht Frankfurt".
With the news that Jupp Heynckes will leave the position as manager, his players marked the new appointment in style as Sandro Wagner grabbed a brace to cancel out Josip Drmic's ninth-minute opener for Monchengladbach.
When it comes to the matches against Real Madrid, the Champions League winners in the past two years, Heynckes admitted to having mixed feelings.
Kovac was appointed at Eintracht in March 2016 and helped the club survive a relegation play-off that season before guiding them to a respectable 11th-place finish in 2017. The top four teams qualify for next season's Champions League group stage.
Kovac will need to adjust to instructing established stars at Bayern, rather than young players of promise still eager to learn, and he will be expected to maintain the club's high standards.
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