The 21-year-old scored 13 goals in 35 Serie A matches this season and will undergo a medical in Turin on Monday.
"Juventus are the side who wanted me the most," he told Sky Sport Italia. "They made a real effort to sign me and this is why I made my decision. I can certainly win the Scudetto there, as they are a winning team. I too always play to win and can find success with them.
"It will be impossible for me to forget everything I've experienced in three years at Palermo. I was happy from the very first day. I know that to play for Juve, I have to do much more and I'm sure I can improve a great deal."
Dybala is hoping to get the chance to play alongside fellow striker Carlos Tevez, but the 31-year-old Teves, who scored 20 Serie A goals this season, has been linked with a return to Boca Juniors.
"I hope he stays, as it would be much easier for me to learn and grow with him by my side," Dybala said.
It is understood that Juventus forked out approximately 40 million euros for Dybala, who signed for Palermo from Argentine second division club Instituto in July 2012 for 12 million euros.
"When I arrived at Palermo, everyone said I was too expensive, but with time I proved that I can play and repeat what I did in Argentina," he said. "It will be the same thing at Juve, people will say the club paid too much, but with a calm mind I will try to repay the Bianconeri."