Italy coach Cesare Prandelli turned to the Roma striker after losing Manchester City's Mario Balotelli and Inter Milan's Giampaolo Pazzini to injury.
Balotelli was ruled out with a back problem, while Pazzini has failed to recover from a foot injury.
"This is a dream come true," Argentina-born Osvaldo told Gazzetta dello Sport. "I want to thank all the Roma fans."
The 25-year-old joined Roma on a permanent transfer from Espanyol last month and has made an impressive start to life in the Eternal City.
He has scored three goals in five league appearances for Roma.
"Osvaldo is of national team calibre," Italy and Roma midfielder Daniele De Rossi added to the newspaper. "He is doing well at Roma and has a lot of confidence in his abilities.
"It could be the start of an important symbol for Roma."
With Zenit St Petersburg defender Domenico Criscito sidelined with a back injury, Prandelli has called Torino defender Angelo Ogbonna up as his replacement.
Ogbonna, who is the only Serie B player in Prandelli's 23-man squad, returns to the national team having earned his first senior call up in June.
The Azzurri are hoping Villarreal forward Giuseppe Rossi, who is struggling with a knee problem, will be fit for Friday's game against Serbia.
Rossi ended Tuesday's training session still hampered by a problem with his left knee that has troubled him in recent weeks.
"He has suffered the same type of problem that he had in Spain," Italy team doctor Enrico Castellacci said. "He has a knee hyperextension.
"He will remain with us and we will decide if he can recover in time for Friday's game."
Prandelli has spoken of the need for the Italians not to lose their focus and to continue playing well, despite having qualification already secure.
The coach will not have Palermo defender Federico Balzaretti, who is doubtful for Friday's match because of a muscle problem.
Italy travel to Belgrade unbeaten in qualifying and with a five-point lead over nearest Group C rivals Serbia, who must win on Friday to secure a play-off berth.
The Azzurri end the qualifying round next Tuesday against Northern Ireland in Pescara.