The 22-year-old Zambia international will move to the King Power Stadium on a five-year contract.
Daka, who was named the Confederation of African Football (CAF) young player of the year in 2017, becomes Brendan Rodgers’ first summer signing and will provide competition upfront for Jamie Vardy and Kelechi Iheanacho.
Daka won the Austrian Bundesliga title with Salzburg last season, scoring 27 goals in 28 games to emerge as the competition’s top scorer. He ended the season with 34 goals in 42 games across all competitions.
"I'm so, so excited to join this great, historic club. It has been my dream and I'm so happy and looking forward to what's coming next," Daka told LCFC TV.
"I have followed Leicester from the time they won the league. I feel it is the perfect place for me, because it's a team that fights for titles. I know it's not going to be easy, but I feel ready to face this new challenge.
"I will give my best for the club each and every day, and I look forward to seeing the Leicester City fans inside the stadium soon."
Daka has made 25 appearances for the Zambia national team, scoring seven goals.
