The 25-year-old midfielder joins the Serie A club after making 177 appearances for Manchester United, with boss David Moyes suggesting it is a good opportunity for the Brazilian
The 25-year-old, who has made eight appearances under David Moyes this season, has joined the Serie A club until the end of the season.
The Brazilian spoke after his first training session with the Viola.
"I'm very happy (to be here)," Anderson told the club's official website. "It is a new challenge.
"I come here to help the team, the players and the manager to do the best.
"I know Fiorentina failed to get in the Champions League last season, so I come to try and help (them get there this season).
"I just want to play, just want to be on the pitch."
Anderson also thanked United for their support during his time at Old Trafford.
"Thank you Manchester United for all you gave to me," Anderson posted on Instagram.
"It was a pleasure and a proud to be part of this tremendous club. I will never forget my great colleagues and friends, all the amazing people that work in the club and obviously the fantastic supporters, always on my side.
"Love you all and you always be in my heart. Wish you all the best because we always be together United family. Now I have to leave because I really need to play.
"Thank you Fiorentina for this opportunity and for believe in me. You won’t regret because you trust me 100% and I will give you 100% of dedication, professionalism and quality. Together we will be happy."
United boss Moyes believes the loan move will be a good opportunity for the Brazilian.
"We've not been able to get him as many games as he'd hoped, or we hoped we might get him," said Moyes.
"We feel it's a good opportunity for him."
The 25 year-old joined United from Porto in June 2007 for £20 million and made 177 appearances for the club.