The fee for Wober, who has signed a four-and-a-half year contract at Elland Road, remains undisclosed.
Wober is the third player Leeds United manager Jesse Marsch has signed from his former club Salzburg since taking charge of the club after Brenden Aaronson and Rasmus Kristensen.
The 24-year-old spent three-and-a-half seasons with Salzburg after joining from Sevilla in the summer of 2019, winning three Austrian league and Cup doubles, and making 125 appearances for the club.
The Austrian international can operate at both centre back and left back.
Wober told Salzburg's website: "It was not an easy decision, but I have decided to leave Salzburg.
"The last three and a half years in this city and at this club really influenced me as a player and a person. The numerous highlights, which I have gained both on and off the pitch, will be remembered by me for as long as I live.
"If I think back to our first season in the Champions League, our very first match in the competition against Genk or our comeback against Liverpool, then it still gives me goosebumps. Thank you for all these moments we have enjoyed together. I have grown to love Salzburg and see it as a second home."
Wober could make his debut for his new club against Cardiff City in the FA Cup this weekend.
