No financial details were disclosed, but Italian media reported that the 27-year-old has joined Simone Inzaghi's side for a fee of around €32 million ($34.94 million), signing a five-year contract.
Pavard, who joined Bayern from VfB Stuttgart in 2019, won the Bundesliga title four times. He also won the 2018 World Cup with France in Russia.
Inter have kicked off their Serie A season impressively, winning their first two matches.
Inter host Fiorentina in Serie A on Sunday.