Pjanic arrived in Turin for his medical on Monday ahead of a proposed move to the Serie A champions.
Vucinic swapped Roma for Juve in 2011 and stayed for three years, and he expects the Bosnia-Herzegovina midfielder to thrive.
"Nothing can surprise me anymore about what happens in the world of football," Vucinic told Tuttosport. "Juventus are strengthening themselves even more.
"Pjanic is an important player. We're talking about a champion, the type that is decisive, and he proved that with Roma.
"For me it was not easy to leave the Giallorossi, I thought about it for a long time. In Rome I enjoyed some great moments, but I have no regrets. I was very happy at Juventus and I won a lot.
"In Rome there is more pressure. But in the Juventus dressing room you can immediately feel a unique winning mentality.
"Even if you snatch a draw at the 90th minute coming from behind, you won't see anyone cheerful or smiling. Instead, everyone is angry, because the only thing that matters is winning."