Boston, which is looking for a starter with Nathan Eovaldi slated to go to the bullpen when he comes off the injured list, also received cash considerations in the deal.
Red Sox president Dave Dombrowski said Cashner would start Tuesday against the Toronto Blue Jays.
The 32-year-old Cashner is 9-3 with a 3.83 ERA in 17 starts for the Orioles this season. He has been hot of late, posting a 1.41 ERA in five starts since the start of June.
He has a 55-82 record in his 10 major league seasons with the Orioles, Rangers, Marlins, Padres and Cubs.
Romero and Prado, both 17, made their professional debuts in the Dominican Summer League. Romero, an infielder, hit .264 with two home runs in 29 games; Prado, an outfielder, hit .303 with nine steals and 26 runs scored in 33 games.