The Uruguay international's exit was finalised after a conversation with head coach Hansi Flick in which it became clear he would not be a regular starter this season.
Araujo will join Liverpool until the end of the campaign, with his contract at Barcelona running until 2031, while the Premier League club have inserted a buy option in the deal worth around €55m (£47m). Liverpool will also cover his full wages for the season, a significant saving for Barcelona given Araujo's salary is among the highest in the first-team squad.
The announcement caught even his Barcelona team-mates by surprise. The centre-back had repeatedly insisted he wanted to stay at the Camp Nou, but changed course after this week's meeting with Flick made his diminished role clear.
His departure was not something the club had planned for, though sporting director Deco had regarded it as a possibility despite Araujo's reluctance to leave.
With Araujo gone, Flick and Deco are now weighing up whether to bring in a replacement centre-back, a scenario that was not under consideration only days ago given the options already available. The head coach can currently call upon Pau Cubarsi, Gerard Martin, Andreas Christensen, Eric Garcia, Jules Kounde and Alvaro Cortes, while incoming midfielder Rodri could also be deployed there if needed.
But with the club targeting the Champions League this season, there is concern over Christensen's injury record, Garcia's importance as cover in other positions, and Cortes' readiness and uncertain long-term future at the club.
Deco has reactivated his search for defensive targets as a result, though any move will depend on how much of the remaining budget is directed towards other priorities, such as the pursuits of Rodri and Julian Alvarez, and on incoming funds from departures including Ferran Torres' move to Paris St-Germain.
Aymeric Laporte's name has circulated in Spanish media in recent days, though no formal talks have taken place beyond an informal meeting between his family and club president Joan Laporta during the World Cup. Cristian Romero, RB Leipzig's Castello Lukeba and Arsenal's William Saliba have also been mentioned in connection with Barcelona, though Deco is understood to be holding other options in reserve that have not yet become public.