Stroppa stepped down from his role in the wake of the Abruzzo outfit's 1-0 defeat against fellow Serie A strugglers Siena on Sunday.
The loss was their third in four league games in a run that has seen Pescara slide into the relegation zone, although it is hoped Bergodi can stop the rot.
"Cristiano Bergodi is the new coach of Pescara," the club said on their official website.
"The signature arrived this morning in the presence of president (Daniele) Sebastiani and director of sport (Daniele) Delli Carri.
"The new Biancazzuro coach will be presented at 1pm (BST) and after that he will travel to the training ground to meet his players."
The 48-year-old represented Pescara for five years from 1984 before he moved on to Lazio, where he made his name with 160 appearances.
After announcing his retirement from playing in 2000, Bergodi went on to manage CFR Cluj and had a temporary spell at fellow Romanian outfit Steaua Bucharest.
He has never managed in the top-flight of Italian football but was in charge of second-tier side Modena last year.