Daka will join the Foxes on a five-year contract, subject to Premier League and international clearance, having enjoyed a stellar goalscoring career with the Austrian Bundesliga side.
The 22-year-old scored 68 goals in 125 games in all competitions for Salzburg, helping them to four successive league titles.
"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."
Leicester will hope Daka can continue his form from last season, which saw him score 27 goals in 28 Bundesliga games.
Only one of those goals came from the penalty spot, with Daka outperforming his Expected Goals (xG) of 22.5 by netting 26 times from 99 non-penalty attempts.
Leicester start their preparations for the new season with a friendly at Burton Albion on July 24. They will face Manchester City in the Community Shield on August 7 before their Premier League opener against Wolves a week later.