The Argentinian completed a move to the Serie A champions following four seasons with Manchester City.
The shirt - made famous by Michel Platini, Liam Brady and Roberto Baggio - has been unclaimed since striker and former captain Alessandro Del Piero left for Sydney FC last summer.
Tevez's transfer fee has not been disclosed but it is reported Juve have paid City an initial £10million, rising to £12million with add-ons.
The 29-year-old told juventus.com: "I'm absolutely aware of the great effort Juventus Football Club has made to bring me here.
"I feel the responsibility of wearing this number and I am aware of the great responsibility of representing Juventus and playing for the club so this number is certainly a great challenge.
"Top players have worn it before and I was number 10 with Boca (Juniors) before, and (Diego) Maradona played in it too, so the great responsibility is now that I'm going to play in this great club so certainly the greatest challenge is to do my best.
"Obviously I didn't want to forget Del Piero who was the last player to wear number 10.
"He is a person and player that I greatly respect and who certainly represents an emblem and symbol of esteem."
Tevez has taken a brief break from his summer holiday in Argentina to join Juve and upon his arrival at Milan's Malpensa airport on Wednesday he was mobbed by around 200 Bianconeri fans.
He is expected to return to South America after Thursday's unveiling to complete his holiday before joining new coach Antonio Conte and his team-mates for pre-season training on July 12.
"I feel the Italian supporters are really similar to the Argentinian ones because they really get involved with the club," Tevez added.
"I was not really surprised by the great welcome I received and I know that the Juventus supporters have showed great love and affection from the very beginning."