Juventus reached an agreement with Barcelona for the €72m transfer of Arthur back in June, with Miralem Pjanic heading to the Camp Nou in a separate transfer.
Arthur joined Barcelona from Brazilian side Gremio in the summer of 2018 and his style of play saw many see him as a long-term successor to Xavi Hernandez.
The 24-year-old made 44 appearances in his debut season and another 28 was taken in last term.
Arthur incurred the wrath of the Barcelona hierarchy when he refused to join their Champions League preparations earlier this month.
Despite the controversial manner of his exit, Arthur has taken time out to say his goodbyes.
"Saying goodbye is always difficult, even more so [because I am] leaving behind a place that has become my home," he said in a video posted to his official social media channels.
"An incredible city that will remain forever in my heart, where everyone received me as another Catalan, showed me a new culture, helped me to grow as a player and, especially, as a person.
"I am leaving a group of brilliant players. I'm very lucky to have played alongside them and, most of all, I am grateful for their support as good people with huge hearts.
"The crowd won me over from the first day, made me proud to play for them and to wear one of the greatest shirts in the world.
"They showed me care and respect that I will never forget. Today is the day to say goodbye, but I am taking everything with me in my heart forever."
Arthur won one La Liga title and one Spanish Super Cup during his time in Spain.
