Upamecano, whose contract at the Red Bull Arena expires in the summer of 2023, has a release clause of £37m and will join the recently crowned FIFA Club World Cup champions on a five-year deal.
The 22-year-old is one of the most highly-coveted young defenders in European football and had interest from the likes of Chelsea and Liverpool.
Bayern Munich are preparing for the possible departures of David Alaba and Jerome Boateng this summer and bringing Upamecano in will go a long way to alleviate the loss of the experienced duo.
When asked whether he could confirm reports that Bayern had won the race for Upamecano, Salihamidzic told Bild: "I can do that, and we are very happy about it at FC Bayern.
"We had very good, intensive and professional discussions with Dayot and his advisor Volker Struth for many months. We knew that we had very strong competition.
"Upamecano is a young player, 22, whose qualities have already developed extraordinarily. I was always convinced that we had presented a good concept.
"We presented him with our vision of his career at Bayern. During the past week in Doha I had further talks with everyone involved. At the end of a long process, the players, family and management were convinced that FC Bayern was the right club.
"Dayot Upamecano will play for Bayern for the next five years."
Upamecano has made 26 appearances in all competitions for second-placed Leipzig this season. He helped the club reach the Champions League semi-finals last season.
