The striker is approaching the end of a six-month deal, having departed St Mary's in January following a training-ground incident.
Osvaldo feels his time at the Serie A champions has been hugely rewarding, and revealed his delight at having scored the winner against former club Roma on Sunday.
"The goal was great, particularly because it has not been an easy year for me," he told JTV. "It was beautiful, especially for the celebration of my team-mates, who have all come together to embrace me, the coach included, and the staff.
"I have so much respect for everyone, this is a fantastic group, sincerely. I am honoured to be a part of this group because it has helped me to grow both as a professional and as a person, whilst this is an experience that I will never forget in my life."
Juventus' win over Roma saw them reach a record-breaking 99 points in Serie A for this season and Osvaldo admits the achievement will be something he will never forget.
"This Juve are now part of history," he added. "This is what we were aiming for [the points record], the most important thing.
"I believe that getting into history at a club like Juventus is not an everyday thing, perhaps it will never happen again, to anyone, or for many years.
"So we have to enjoy this moment because we have done something spectacular."
Osvaldo has scored three goals in 17 appearances for Juve.