Montella has signed a two-year contract with the Tuscan club with an option for a third year.
"Forentina convinced me (to sign) because they want to be great again, to return to the part of the league table where they belong, and I feel the same desire," the former Roma striker told a news conference.
"The club have shown me great respect and this motivates a great feeling of responsibility in me because Florence is a great place."
Montella said he wanted to bring Fiorentina back to the top of the table after a difficult year in which they were threatened with relegation to Serie B.
Last season was marked by frequent fan protests and a plunge in attendances as fans lost faith in the team.
"The club have asked me to recreate enthusiasm for the team, we want to bring ourselves closer to the supporters," he said.
Montella replaces Delio Rossi, who was sacked towards the end of last season after punching his own player Adem Ljajic during Fiorentina's 2-2 draw with relegation rivals Novara.
He had an impressive season with Catania, guiding them to a comfortable mid-table finish and playing an exciting brand of football in the process, and he had been linked with the AS Roma job after Luis Enrique's exit.
However his former club chose the flamboyant Zdenek Zeman, another manager who favours an attacking style of play.
Catania announced the signing of Rolando Maran, who lost the Serie B playoff final to Sampdoria with Varese this weekend, as Montella's replacement on Monday.
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