Zeman quit his post at the Serie A strugglers on Tuesday, ending his second spell of the campaign at the Sardinian club, and Festa has assumed control for the closing weeks of the season.
Festa – who started his playing career at Cagliari – will be assisted by David Suazo and Gustavo Aragolaza, Gianfranco Ibba and Giomaria Ruiu as he looks to lift the club out of the bottom three.
With seven games to go, Cagliari are 19th in the league table and nine points from safety.
Festa, 46, is the club's third different coach of the season, with another fomer fans' favourite Gianfranco Zola having endured a torrid 11-game spell at the helm.
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