Demichelis replaces Ole Werner, who was sacked last week, despite Leipzig finishing third in the Bundesliga last season and qualifying for next season’s Champions League.
The Argentine is RB Leipzig's eighth permanent head coach since the club's promotion to the Bundesliga in the 2016-17 season.
Demichelis began his coaching career as an assistant at Malaga and also worked with Bayern's youth teams. He took on his first senior managerial role at boyhood club River Plate for the 2022-23 season, guiding the Buenos Aires side to the Argentine league title.
He was most recently in charge of relegation-threatened Spanish side Mallorca, taking over in February until the end of the season. Despite five wins and an eight-game unbeaten run, Demichelis was unable to keep the club in La Liga.
"RB Leipzig are an ambitious club with a clear identity, outstanding talent and a determination to keep improving at the highest level. That is exactly the kind of challenge I was looking for," the 45-year-old said in a statement.
"I’m also really looking forward to leading RB Leipzig in the Champions League. Testing ourselves against Europe’s best is an incredible challenge and exactly where a club with RB Leipzig’s ambition and quality belongs. I can’t wait to share those special nights with the team."
Demichelis spent the majority of his playing career with Bayern Munich, making 259 appearances for the club and winning four Bundesliga titles and four German Cups.
He also played for River Plate, Malaga, Atletico Madrid, Espanyol and Manchester City, where he won the Premier League in 2014. He has 51 senior caps for Argentina's national team, and was a World Cup runner-up in 2014.