The 18-year-old defender has put pen to paper on a four-and-a-half-year deal after a reported initial fee of €10 million was agreed between the clubs.
"We are delighted that Dayot decided to join us to make the next step in his career, despite several offers from top international clubs," Leipzig sporting director Ralf Rangnick said via the club's official website.
"We are convinced that Dayot can already be a reinforcement for the first-team squad in the near future.
"Dayot has shown a great deal of promise for his age and we think he will fit in perfectly with the philosophy of the club."
The centre-back, who has represented France from Under-16 through to U-19 level, has made 21 appearances this season for Salzburg.