"We are very happy that we could secure Niko Kovac's services", he said.
Bobic also spoke about the exit clause that was triggered by Bayern, saying: 'Yes, there was an option for Niko Kovac to get out of the contract if an absolute European top club came. "We are convinced that he is the right coach for Bayern's future".
Kovac will be joined at Bayern by his younger brother Robert as assistant coach.
The 46-year-old, who had a long playing career in the Bundesliga, was at Bayern between 2001-3.
"The offer has surprised us at this stage of the season, but we owe a lot to Kovac", Bobic told reporters at a news conference on Friday. They are back in the last four of the German cup.
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But Kovac places huge value on the personal relationship with his players, a quality he attributes to his former coaches Ottmar Hitzfeld, Giovanni Trapattoni and Christoph Daum ("Three coaches who also possessed great human qualities in addition to their professional expertise") but also to his strong Christian faith.
Bayer Leverkusen underlined its Champions League credentials with a 4-1 win over Eintracht Frankfurt, while Hamburger SV and Cologne edged closer to Bundesliga relegation on Saturday. "You can't buy the Champions League these days".
Germany global Wagner proved a capable deputy for Robert Lewandowski, who dropped to the bench as one of seven alterations from the side that clinched a Champions League semi-final spot with a 0-0 draw against Sevilla on Wednesday, with two goals in the space of four first-half minutes. "A enormous fixture, in a very positive way", he said.
Former Borussia Dortmund coach Thomas Tuchel had already turned down Bayern and is expected to be the next coach of Paris Saint-Germain.
The 72-year-old will end his third spell in charge of the club this summer and there has been much discussion surrounding who will take over at the end of the season.
Heynckes is now the Bayern Munich coach (again).
Gladbach opted to play on the counter-attack thereafter and Wagner punished their reluctance to get forward with a pair of strikes, the second of which Yann Sommer should have done more to keep out.