The much-awaited ABC TV drama premiered in the US on Sunday. The first episode of "Quantico" will air in India on October 3.
The New York Times praised Chopra as the "strongest human asset in Quantico".
"Ms Chopra, a Bollywood superstar and former Miss World is immediately charismatic and commanding amid the otherwise generic ensemble. If there is a problem with her casting, it is that she may come across as too seasoned and assured to be persuasive as a shaky, neophyte recruit."
The Wrap called Chopra as someone having "a poise and sexual spark as Alex that suggests a formidable potential FBI agent whose mind and beauty are equally stunning".
Even fans of the 33-year-old actress took to Twitter to appreciate her latest international stint.
"@priyankachopra Next big star," a fan said. Another added, "Cool seeing it say "Starring Priyanka Chopra." #Quantico @priyankachopra.