The former France international says he believes the Bianconeri have the ability to win the competition, after joining on loan from Shanghai Shenhua until the end of the season
The ex-France international made 22 appearances for the Chinese club, where he linked up with former Chelsea team-mate Didier Drogba, since joining in January 2012.
And he now believes his new side are capable of lifting the European trophy.
"I believe a team like Juventus has the players, mentality and athletic qualities required to [win the Champions League]," the 33-year-old told Juventus' official website.
"We'll give all our strength and energy to bring the trophy home."
But he added: "It's a very difficult competition. When you start out you never know if you'll be able to win it, but you still need to go for it all the same."
The former Chelsea and Liverpool attacker also said he was happy to be part of the Italian side's team, adding: "I've joined a great club with great players.
"I'm happy to be here and to share these moments with them, and I'm very proud to be able to wear this shirt.
"[My former France team-mates, such as Lilian Thuram and David Trezeguet] have spoken to me about it [playing at Juventus]. They've told me it's a great club and it's like a family.
"When I arrived, I got that feeling straight away. When I walked into the dressing room, they all gave me a warm welcome and made me feel at home.
"Italian football is renowned all over the world. It's a league with great players, very physical and combative, as the current table suggests. I'm here to help last year's Scudetto winners reclaim the title."
The former Arsenal and Real Madrid star also spoke about his experience in China, where he spent time as both a player and coach since his move from Chelsea.
"It was good, I lived in a magnificent city," said Anelka. "It was a slightly complicated experience as far as their approach to the game was concerned. But I still appreciated it a great deal and have no regrets," he added.