Juventus director Fabio Paratici said Miralem Pjanic would only leave for Barcelona after the Bosnian midfielder agreed to join the LaLiga champions.
Pjanic will swap Juve for Barca at the end of the 2019-20 season, with Arthur moving in the opposite direction as part of the high-profile swap deal.
Juve star Pjanic was in the starting XI and played 74 minutes of Tuesday's 3-1 Serie A victory over Genoa following the announcement.
Asked about Pjanic prior to Juve's win, Paratici told Sky Sport Italia: "Logically, the transfer market is part planning and part opportunity. In this particular deal, we had both elements.
"Pjanic is a very important player for us, so when the option emerged, we spoke to Miralem and he said he was happy here, so the only club he would've left us for was Barcelona.
"We found this player Arthur, who we had been tracking for a long time, and who is younger than Pjanic."
Juve have also been involved in another swap deal, with 19-year-old Portuguese winger Felix Correia arriving from Manchester City in exchange for 18-year-old Spanish forward Pablo Moreno.
Correia has signed a five-year contract in Turin following his €10.5million (£9.5m) transfer, while Moreno – who left Barcelona for Juve in 2018 – has penned a four-year deal and cost City €10m (£9m).
"Felix is a winger who is strong in taking men on, he's very talented and we'd been following him for a while too," Paratici added. "He was more functional for our U23 team project compared to Moreno."