Flower departs after two years in charge during, which Lucknow made the playoffs and finished third on both occasions.
"Lucknow Super Giants are on the journey of building a great story in the IPL," former Australia test batsman Langer said in a team statement.
"We all have a role to play in that journey and I am excited to be a part of the team moving forward."
Langer, the coach when Australia won their maiden T20 World Cup title in 2021, he stepped down from that role in 2022, rejecting a short-term extension offer.
Under him, Perth Scorchers won the Big Bash title three times.
Franchise owner Sanjiv Goenka said: "I have enjoyed my interactions with Justin Langer. He seems to bring in a huge amount of aggression and a lot of clarity."