Gasperini was sacked by Rosanero president Maurizio Zamparini as the Sicilian club sank to the bottom of the Serie A table with defeat to Atalanta on Sunday.
A statement published on palermocalcio.it read: "Palermo have entrusted the care of the first team to Alberto Malesani.
"The 59-year-old coach is taking his first training session now and will be presented at Boccadifalco tomorrow [Wednesday] morning."
Palermo are currently four points from safety with 15 games left to salvage a top-flight status they have held since 2004.
Gasperini, who had only replaced Giuseppe Sannino in September, delivered just three wins and 15 points from his 20-game tenure at the Renzo Barbera.
President Zamparini has developed a reputation as an impatient employer since purchasing Palermo in 2002 but he decided to invest heavily in Gasperini's project, allowing the ex-Inter Milan boss and director Pietro Lo Monaco to sign 10 players in the January transfer window.
Reports in Italy suggest Lo Monaco has also left the club in the wake of Gasperini's dismissal with former Palermo director Giorgio Perinetti set to replace him.
Malesani made his name with Parma, with whom he won the Coppa Italia, UEFA Cup and Supercoppa at the turn of the century, before arriving at Greek club Panathinaikos via spells with Verona and Modena.
After losing his job in Athens Malesani returned to Italy to coach Udinese, Empoli and Siena before keeping Bologna in the top flight at the end of the 2009-10 season.
Two ill-fated spells with Genoa followed. Malesani was sacked by the Rossoblu in December 2011 - six months after accepting the job - only to replace his successor Pasquale Marino in April 2012.
He was dismissed once again when a 4-1 home defeat to Siena left Genoa one point above the relegation places and inspired mass protests from fans at the Stadio Luigi Ferraris.
Quoted in Gazzetta.it on Tuesday, Malesani said: "I'm happy to be here. I will speak to the players to see how they feel, I only want guys who love the shirt.
"Surviving will be a tall order but we want to succeed. I am confident. I will have the same staff I had at Bologna and they will all focus on keeping us up."