River Plate's highly-rated teenage midfielder Erik Lamela
"Lamela is now a Roma player," said River Plate president Daniel Passarella Passarella.
Lamela, 19, signed a five-year deal in the Italian capital worth 1.5 million euros a year.
The Italian news agency ANSA said that the fee for the deal is 20 million euros, including bonuses and tax.
Lamela played 36 times for River Plate last season, scoring four goals.
The most successful club in the history of the Argentine game, River were relegated to the second tier for the first time last month, and are now looking to sell their leading young players in order to raise funds in the face of a growing financial crisis.
As Lamela heads for Serie A, he becomes the fourth signing made by Roma since the club were taken over by Italian-American businessman Thomas Di Benedetto.
He follows in the footsteps of Spanish full-back Jose Angel, recruited from Sporting Gijon, young French defender Loic Nego from Nantes, and Barcelona striker Bojan Krkic.
Roma also have a new coach, in the shape of former Barcelona B boss Luis Enrique.