The 23-year-old has signed a five-year contract with the Tigers until 2031, becoming their 10th summer addition.
Gourna-Douath made 95 appearances during his four years at Salzburg, including 24 in European competition, and helped the club win the Austrian Bundesliga in 2022/23.
“I’m really happy because it was such a long journey from the first phone call until I signed. I’m so excited to get started,” he said.
“I know Hull City is a big family club. Playing in front of our fans will be fun. It will be amazing for me.
“The Premier League is the best league in the world. I’m really happy and really excited to face those teams with Hull.
“I love fighting to win the ball back and having the ball at my feet to make the team play. I love to play for the badge and for the fans.
The defensive midfielder began his career at Saint-Étienne, where he made 65 appearances before joining Salzburg in 2022.
Gourna-Douath has represented France from Under-16 to Under-21 level, making 34 appearances and captaining his country at four youth age groups.