The Italy international striker completed his loan move to the reigning Serie A champions from Southampton on transfer deadline day, with the league leaders retaining the option to purchase the forward at the end of the season.
Osvaldo had previously been used to battling Antonio Conte's side after a two-year spell at Roma, before making a reported €15.6 million (£12.8m) switch to the Premier League in August.
After scoring just three goals in England's top flight, Osvaldo received a two-week suspension for a reported attack on team-mate Jose Fonte which prompted his exit from St Mary's, but the 28-year-old says he is honoured to have joined the Scudetto favourites.
"[Juventus] were devastating [to play as an opponent]," he told the club's official website. "I found it a really tough experience. I hope I can now enjoy being on the other side.
"I hope to bring plenty of excitement. I want to enjoy this personal moment. It's an honour and a dream to be here at Juve.
"Both the team and I will focus solely on doing things well and the rest doesn't matter."
Osvaldo believes the fact he is familiar with many of Juve's first-team squad will help him settle, and says he is thrilled to be linking up with fellow striker Fernando Llorente following their respective spells in La Liga.
He added: "We know each other. Fernando is a great guy and an exceptional player.
"I already know most of the lads here and that's something that will certainly help me a great deal."