The 25-year-old has been an infrequent presence since David Moyes took over at Old Trafford, starting only three games and making five further appearances off the bench.
He had not been involved since the 2-0 win over Stoke a month ago and now hopes to help his new side reach the Champions League, joining Alessandro Matri and Antonio Rosati in boosting their squad.
Fiorentina sit fourth in Serie A, five points behind third-placed Napoli and 15 off leaders Juventus.
Anderson said: "I was happy at Manchester for seven or eight years, it was a big club for me... but now it's a new challenge and the time to change.
"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'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 only missed out on the Champions League by two points last season, so this year I want to help them get into the Champions League."
The Brazil international arrived at Old Trafford in 2007 from Porto and made 179 appearances for United in all competitions.