The 19-year-old midfielder left Manchester United this summer to sign a four-year contract with the Turin giants as a free agent.
Pogba is rated as one of the more promising young players in European football and is keen to prove himself as a valuable asset to the Italian champions.
"I've been compared to Vieira and it's a compliment as far as I'm concerned," the Frenchman told Juve's official website.
"I hope to maybe become even stronger than he was, taking some of his best qualities, but also offering something different as Pogba and not Vieira.
"I'm really happy to be here and proud to wear the black and white colours."
Pogba further expressed his enthusiasm at joining Juventus.
"I'm so happy to have seen the Juventus Museum and be able to fully appreciate the club's history," he added. "I've noticed there are many champions who have played for this team and I hope that I'll be able to form part of this group of champions to share its history in the future.
"I'm happy to be here, it's a real honour. Among the former players I was particularly inspired to see Michel Platini, Pavel Nedved and Roberto Baggio. From the current crop I'd say Andrea Pirlo, Gigi Buffon, Claudio Marchisio and also Giorgio Chiellini.
"They're all quality players and I've got a great desire to play alongside them. I hope it all goes well and I'm able to forge a good understanding with everyone."