The Catalans say Arthur's fee will rise to €82m (£75m) after an initial payment of £66m.
In the meantime, the 23-year-old vowed to "give everything" to his current club for the rest of the season.
Speaking at a news conference on Monday, prior to the confirmation of the deal, Juve coach Maurizio Sarri said he had no doubts Pjanic would give his all to the cause before heading to Barca.
'FC Barcelona and Juventus FC have reached an agreement for the transfer of player Arthur Melo.
Sarri had expressed a desire to see Pjanic remain with the Bianconeri beyond the end of the season.
Arthur joined the reigning LaLiga champions from Gremio in 2018 and has gone on to make 72 appearances for the club, winning the league title and the Spanish Super Cup in his first season. He signed a five-year contract with the eight-time defending Serie A champion. The purchase value may increase of maximum 10 million euros on achieving given conditions during the course of the contract.
The Bosnia and Herzegovina global joined Juventus from Roma in 2016, helping the Bianconeri win the Italian Serie A title three times.
Last year, Barcelona carried out a similar transaction by exchanging goalkeeper Jasper Cillessen for Valencia's Neto, in deals worth around 30 million euros each. "The Italian club will pay 72 million euros, plus 10 million euros in variables", read a Barcelona statement. The Brazilian midfielder has played 72 games for Barcelona until now.