The 54-year-old Frenchman will join the Italian team on January 9 as a replacement for Mattia Binotto.
Binotto is stepping down at the end of the year after a campaign which saw a catalogue of Ferrari errors harm Charles Leclerc's hopes of winning the driver's title.
Binotto will be succeeded by Vasseur, who in six seasons with Alfa Romeo led the team from bottom of the constructors' championship to sixth this last year - their highest finish since 2012.
Vasseur said: "I am truly delighted and honoured to take over the leadership of Scuderia Ferrari as team principal.
"As someone who has always held a lifelong passion for motorsport, Ferrari has always represented the very pinnacle of the racing world to me.
"I look forward to working with the talented and truly passionate team in Maranello to honour the history and heritage of the Scuderia and deliver for our Tifosi around the world."