The 25-year-old, who has been at Old Trafford since 2007, took part in his first training session with his new club on Saturday after agreeing a move until the end of the season and passing a medical.
The Brazilian has failed to establish himself as a regular in the United midfield and in the summer he will have just one more year on his contract.
Anderson told violachannel.tv:
“The team look after me, everyone is trying to help me adapt to Italian football. I appreciate what everyone is doing for me, it’s very nice.
“I am very happy. I am very happy in Manchester United as well, it’s a big club for me. I’ve been there for seven or eight years, I have a lot of friends and family there. Now it’s a new challenge.
“I’ve come here to try to help the players, try to help the team, try to help the manager and do my best.
“I know last year Fiorentina missed out on the Champions League by two points. This season they are trying to get in the Champions League, I have come here to try to help.”