Digne becomes Barca's second signing in as many days, and their third in the current transfer window after landing fellow Frenchman Samuel Umtiti and Denis Suarez.
The 22-year-old left-back spent last season on loan at AS Roma, where he faced Luis Enrique's side in the UEFA Champions League group stages, and arrives at the Camp Nou for a fee of R261-million.
The club has confirmed that Digne will sign a five-year contract, upon his completion of a medical after his arrival in Catalonia on Thursday morning, with his buy-out fee set at R950-million.
"FC Barcelona have reached an agreement with Paris Saint-Germain FC to sign the 22 year old French player Lucas Digne for the next five seasons," read a statement on Barca's website.