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.
"What Fredi Bobic said was outrageous", Hoeness told Sky Sport Germany.
Kovac will also bring his 44-year-old brother Robert Kovac from Frankfurt as assistant coach.
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 former Chelsea and Real Madrid boss was heavily criticized by the fans, critics and even the Bayern Munich president before eventually being fired by the club.
Rummenigge also defended Bayern, adding: "I have to say that, from our point of view, there are no irritations. Not of Eintracht Frankfurt". "Not of Eintracht Frankfurt".
Kovac arrived at Frankfurt in 2016 and has led them from the brink of relegation to a possible European spot for next season with them sat in sixth and five points off Bayern Leverkusen.
It his highly expected Unai Emery will stand down or be sacked at the end of the season following another disappointing Champions League campaign, and Tuchel had been heavily tipped for the job.
Frankfurt also has a German Cup semifinal match against Schalke next week.
Hoeness was particularly angered by suggestions that Bayern intentionally leaked the news of Kovac's appointment to the press. Bayern's loss is Hoffenheim's gain, however, as the young coach can continue to build his team to climb the Bundesliga table. "Everyone respects the other", Frankfurt forward Kevin-Prince Boateng said earlier this season. I informed the team this morning.
Heynckes returned in an interim capacity - his fourth time in charge of Bayern, with the previous three reaping a Champions League title as well as four Bundesliga crowns and a DFB-Pokal - in October 2017 after Carlo Ancelotti was sacked.
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.