The 24-year-old Denmark international has signed a five-year contract at Elland Road and becomes Jesse Marsch's second summer signing after Brenden Aaronson, who also joined from Salzburg recently.
Like Aaronson, Kristensen also played under Marsch at the Austrian champions.
The right-back joined Salzburg from Ajax Amsterdam in 2019, winning three Austrian top flight titles and three Austrian cups.
A statement from the Premier League club read: "Leeds United are pleased to announce an agreement has been reached with Red Bull Salzburg for the signing of Rasmus Kristensen, which will be completed on July 1st 2022.
"The Whites have beaten off competition for the 24-year-old, who will join for an undisclosed fee and has accepted terms on a five-year-contract at Elland Road, running until the summer of 2027."
“When I heard about the interest I looked at the project and what was going on and I was never in doubt, I was 100 per cent convinced,” Kristensen told LUTV on his move to the Premier League team.
“It’s a huge historical club which is playing in the best league in the world and for me, it fits everything that I love about a football club.
"I know a lot of things about the club, where I am from, a small village, most of my father’s mates are Leeds fans.
"I want to compete against the best and I will do that here.
"I see myself as a physical, emotional power player, I like to go forward, run up and down the flank and I have a big engine for that.
"I’m a guy who puts 100 per cent effort in every time I’m on the pitch and I’ll die with my boots on.
"It’s been a great few days with the national team, playing games, flying in and out, it’s been busy but good.
"With the national team having four games in the Nations League, it fit in perfectly to come to Leeds in-between the two days with a day off from the national team coach, so I’m pleased and happy that everything is settled and everything is done."
Leeds will be looking to improve next season after flirting with relegation and ultimately finishing 17th in the 2021/2022 campaign.
Kristensen has won six caps for the Denmark national team.
