The Argentina-born attacker was desperate to leave Southampton after just six months at the club and accepted lower wages to facilitate his move to the Old Lady
The Italy international joined Juve on loan until the end of the season on deadline day of the transfer window, after a training ground bust-up with Jose Fonte saw the club suspend him for two weeks.
And Conte has now revealed the full extent of Osvaldo's desire to move to Turin and is hoping the Italy international will bring variety to his attacking options.
"We grabbed an opportunity to sign him," Conte told Sky Sport Italia.
"The player really wanted to come to Juventus and actually significantly reduced his demands to secure the move.
"He’ll improve the quality of our attack and offer important competition to those already here."
The 28-year-old had only joined Southampton from Roma at the start of the 2013-14 campaign, but scored just three times in 13 league appearances.