"Niko played for Bayern, and knows the people in charge, as well as the structures and DNA of the club very well", Salihamidzic continued.
The 46-year-old Croatian will start a three-year contract from July 1, the club announced just minutes before Friday's Champions League semi-finals draw which left the Bundesliga champions pitted against holders Real Madrid.
The 46-year-old Kovac, who spent most of his playing career as a central midfielder in Germany, was a Croatian worldwide and formerly guided the Croatian national team.
At a news conference later Friday, the older Kovac said he had mixed feelings about leaving Frankfurt, but "not many coaches, not many players" get an opportunity at Bayern.
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. But Heynckes' long-term assistant and former Fortuna Düsseldorf manager Peter Hermann will remain to support Kovac, who will also be accompanied by his younger brother Robert and Armin Reutershahn, his two Eintracht assistants. This season, only Bayern and Schalke have better defensive records than Eintracht while only Hoffenheim have received more yellow cards. "We're convinced he's the right coach for the future of FC Bayern".
The Colombian is now on two-year loan at the Bundesliga club.
Roma's sporting director Monchi said: "This seems the ideal opportunity to achieve the happiness that we couldn't get all those years ago".
Kicker magazine reported that Bayern would pay a fee of 2.2 million euros ($2.7 million) to trigger a release clause in Kovac's existing contract with Frankfurt.
"There was no contact between the clubs", Bobic added. "I was really impressed", he said.
Kovac's first senior coaching job came with the Croatia national team, whom he led at the 2014 World Cup.
Danny Murphy wishes Real Madrid had drawn Liverpool in the last four though.
Roma produced one of the most memorable reversals in Champions League history to knock out Lionel Messi's Barcelona with a 3-0 victory in the Italian capital that gave them an unexpected win on away goals over the two legs.
Thomas Tuchel was reportedly in the running for the vacancy only for Bayern CEO Karl-Heinz Rummenigge to confirm the former Borussia Dortmund coach - strongly linked with Paris Saint-Germain - has agreed to move elsewhere.