Celestini arrives to take charge of a Clarets side who have started life back in the Championship badly, having won just once in the league this season to leave them in 22nd position in the table.
Their poor form stretches back to a torrid Premier League campaign last term, and the club are without a win at home in the league for over a year.
Earlier this week, Diego Lopez was appointed as director of football and given the task of finding a new manager after Hayen left in the aftermath of Saturday’s 4-1 defeat by Lincoln City.
“Fabio brings the passion, experience and knowledge we were looking for,” Lopez said.
“He showed extraordinary determination and conviction to come to Burnley.
“We want people who truly want to be here and help this club grow. Fabio is a clear example of that.”
Details of Celestini’s contract have not been disclosed by the club.
A former midfielder who won 35 caps for Switzerland, he began his managerial career with Italian club Terracina.
As well as Basel and CSKA Moscow, he has also had spells at Lausanne – his principal club as a player, Lucerne, Lugano and Sion.
He left CSKA by mutual agreement in May after 11 months with the Russian Premier League side.
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