The 24-year-old, who can operate at both centre-back and left-back, is Leeds' first signing in the January transfer window after agreeing a four-and-a-half-year deal.
Leeds said in a statement: "He now links up once again with head coach Jesse Marsch (at Elland Road) along with his former Salzburg team-mates Brenden Aaronson and Rasmus Kristensen.
"Wober will wear the number 39 shirt during his time at Leeds and could feature for the first time in Sunday's FA Cup third-round tie at Cardiff."
Marsch spent two years in charge at Salzburg until 2021, while Leeds signed USA forward Aaronson and Denmark defender Kristensen from the Austrian club last summer.
Wober, who has made 13 senior appearances for Austria, started out at Rapid Vienna and joined Ajax in 2017 before moving on to Sevilla, initially on loan, in early 2019.
He became the Austrian Bundesliga's most expensive signing in August 2019 when joining up with Marsch at Salzburg and went on to make 125 appearances in all competitions for the club.
During his time at the Red Bull Arena, Wober won the Austrian league and cup double three times in a row.