The 45-year-old Argentine arrives from RCD Mallorca, where Leipzig triggered a €2.5m release clause to secure his services. He replaces Ole Werner, who was dismissed after a single season despite leading the club to third place in the Bundesliga and Champions League qualification.
Demichelis had signed a contract extension with Mallorca just three weeks prior to his departure, but RB Leipzig moved quickly once the decision to part with Werner was made. He becomes the first Argentine to take charge of the Red Bulls in the Bundesliga.
"I was convinced by my discussions with the club and its sporting vision," Demichelis said in his official presentation.
"RB Leipzig are an ambitious club with a clear identity, outstanding talent and a determination to keep improving at the highest level.
"That is precisely the kind of challenge I was looking for."
He added: "I want to create a side that plays bold, intense and exciting football, takes responsibility on the pitch and inspires the people of Leipzig with its passion."
Managing director of sport Marcel Schäfer cited Demichelis's international background as central to the decision.
"Martín brings experience of working at the highest level as both a player and coach in Europe, South America and North America," Schäfer said. "That international perspective is an excellent fit for RB Leipzig and our global outlook. We are convinced he will give the team important new impetus."
Demichelis won four Bundesliga titles across almost eight seasons at Bayern Munich as a player, and also won a Premier League title with Manchester City. He later led River Plate to an Argentine league title before taking on his first European head coaching role at Mallorca.