The 24-year-old striker inherits the Number 11 shirt Werner vacated when he left to join Chelsea last month.
Hwang has signed a five-year contract. "He fits perfectly into what we require, can play any position in attack, on the wing or acting as a central striker," said Leipzig sports director Markus Kroesche.
"With his speed and agility he makes our attack even more flexible."
However, Leipzig pointed out that Hwang has signed for 2020-21 and is "not available" for the Champions League finals in Lisbon next month.
Leipzig, who finished third in the Bundesliga last season and knocked out Tottenham in the last 16, will discover their quarter-final opponents in Friday's Champions League draw.
The South Korean international scored 16 goals, creating 22 assists in helping Salzburg win the Austrian league and cup double last season.