The LaLiga champions have sanctioned a deal to allow Araujo to move on for the 2026/27 campaign as he's no longer a regular starter for Hansi Flick in Catalonia.
Liverpool will cover Araujo's full wages during his loan at Anfield and Andoni Iraola has been offered a non-mandatory €55M purchase clause on the Uruguay international.
Araujo was excused from Flick's preseason squad which travelled to Italy and secured a 1-0 wins over Nottingham Forest, but lost out to hosts Udinese.
Flick was asked about Araujo's departure after the double header and he confirmed the 27-year-old is excited by the move to England.
"He's a great guy and a fantastic player. But his style of play is different from what I prefer. He's powerful, fast... it's a shame. It's been difficult because I haven't been able to include him as much as I'd like.
"He's been affected by past mistakes. We've talked. I saw him feeling very good as he left and I wish him all the best. Changes are normal in life and in football.
"There's a lot of noise around transfers. We know what we want and we want to improve the team. Many of our players will arrive back next week. This preseason isn't normal; there's very little time to work with the squad."