Pavard emerged as one of the stars of France's World Cup triumph in Russia, playing in six matches over the course of the tournament at right-back, including the full 90 minutes in the 4-2 win over Croatia in the final.
Levelling the game up at 2-2 at the time, Pavard smashed a stunning volley past Franco Armani in the Argentina goal, with France eventually going on to win 4-3.
Wednesday's announcement means that, after completing the 2018-19 season with Stuttgart, Pavard will join Bayern in the summer.
Salihamidzic revealed to reporters: "I can confirm that Benjamin Pavard will join us on a five-year deal from 1st July 2019.
"Pavard is a young player and a world champion. We're delighted and very proud to have been able to secure the services of a player like him."
Bayern are currently on their annual winter training camp in Doha as they prepare for the second half of the Bundesliga campaign.
Niko Kovac's side trail Dortmund by six points in the table - the first time in eight seasons that they have not led the way going into the winter break.
And the signing of Pavard is unlikely to be the final piece of business completed by Bayern in January.
As revealed by Goal , the Bavarians have made a fourth bid of £35m ($45m) for Chelsea winger Callum Hudson-Odoi , offering him the No.10 shirt in an attempt to convince him to move to Germany.
Kovac's side had already completed the $13.5 million (€11.5m/£10m) signing of Alphonso Davies from Vancouver Whitecaps, with the 18-year-old Canadian part of the 29-man squad that travelled to Qatar on January 4 .
Bayern resume the Bundesliga season with an away trip to Hoffenheim on January 18, while Pavard's current side Stuttgart, who are 16th in the table, host Mainz on January 19 as they aim to move further away from the relegation spots.