Rossi and Osti were hired in December to replace tactician Ciro Ferrara and official Pasquale Sensibile.
The duo, who also worked together at Lecce in the past, have put pen to paper on new deals until June 2015.
Newly promoted Sampdoria were facing a relegation battle, but results significantly improved once Rossi took over.
Rossi, 52, has recently bossed Lazio, Palermo and Fiorentina in the top flight.
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