The fullback spent last season on-loan at PSV, though his season was curtailed by knee injury.
Barca have now granted Dest a free transfer to PSV, though will retain a percentage of any sell-on fee.
They announced: "FC Barcelona and PSV Eindhoven have reached an agreement for the transfer of the player Sergiño Dest. FC Barcelona retains a percentage of any future sale.
"Thank you very much, Sergino".
Dest also said: "First of all, PSV believes in me and I am very much appreciated here. I have experienced an incredibly warm club, like I have never experienced anywhere before.
"These are important aspects for someone in my situation and give me confidence that I can recover well here. Once my time came, it was very nice to see that the game we are looking for here really suits me. I really can't wait to play for PSV again, to be important and to win titles."