The 24-year-old has signed a five-year deal for Julian Nagelsmann’s men and will take over the number 11 jersey, which has been vacated by Chelsea-bound Timo Werner.
Hwang impressed for Leipzig in the 2019/2020 season as he courted attention from some of Europe’s biggest clubs with his displays in the group stages of the Champions League alongside the likes of Erling Haaland and Takumi Minamino, who have since joined Borussia Dortmund and Liverpool respectively.
One of his three Champions League goals this season came at Anfield and he found the back of the net 16 times in 40 appearances across all competitions.
This will be Hwang’s second spell in Germany, having spent a season on loan at Bundesliga 2 side Hamburg in the 2018/2019 season.
"In Hee-chan Hwang we have signed a player who fits the profile of what we are looking for," Leipzig sporting director Markus Krosche explained to the club's official website.
"He can play in any attacking position, on the wings or as a main man in the middle. He makes our attack more flexible with his speed and mobility. He had a great season in Austria, as both a goalscorer and provider, and he particularly impressed in the Champions League.”
Hwang added: "I’m excited for the new challenge at RB Leipzig! I want to help the team continue to be as successful as possible and achieve this young club’s ambitious goals.
"The club’s aims and style of football are both perfect for me. I want to take my next step as a professional here in Leipzig. On top of that, I want to score as many goals as possible."
Hwang departs Salzburg with a league and cup double from this season.