Germain for £13.9m (16.5m euros).
The 22-year-old, who played 33 times for Roma last season during a loan spell, joins on a five-year deal with a buy-out clause of £51m (60m euros).
He made 44 appearances for French champions PSG following his 2013 switch from Lille.
Digne, who has won 13 caps, was part of the France squad to reach the Euro 2016 final, but he never made an appearance.
He is the second Les Bleus international to join Barcelona this summer after the arrival of fellow defender Samuel Umtiti from Lyon.