Puel, who was previously in charge at Nice between 2012 and 2016, "begins today his priority mission of improving the team's performance," Nice said in a statement.
Nice thanked Haise and his assistants "for their commitment and the work accomplished in the red and black colours and wishes Claude Puel a good return to the bench."
Puel spent his entire playing career with neighbouring Monaco before becoming manager of the club.
He then went on to manage Lille, Lyon and Saint-Etienne in Ligue 1, and Southampton and Leicester in England's Premier League.
Nice currently sit 13th in Ligue 1.
The Mediterranean team beat second-division Saint-Etienne in the French Cup last week to snap a club record nine-game losing streak.
Puel's naming comes less than 10 days after the return of former manager and club president Jean-Pierre Rivere to replace Fabrice Bocquet as club chief executive officer.
The club is owned by INEOS, the company of the British entrepreneur Jim Ratcliffe, who also has a 25 per cent stake in Manchester United.
In November, players, staff, and management had a run-in with 200 fans gathered in front of the training centre to express their anger at the Nice squad as it returned from a 3-1 loss at Lorient.
The club returns from their brief winter break with a home match against Strasbourg in Ligue 1 on January 3rd.