Ferrari team principal Marco Mattiacci hailed the arrival of Vettel, who will partner Kimi Raikkonen in 2015, and predicted he will become an "invaluable" asset.
"Scuderia Ferrari has decided to put its faith in the youngest multiple champion in the history of Formula One," Mattiacci said.
"In Formula One terms, Sebastian Vettel is a unique combination of youthfulness and experience and he brings with him that sense of team spirit which will prove invaluable when, together with Kimi, they tackle the challenges awaiting us, as we aim to be front runners again as soon as possible.
"With Sebastian, we all share a thirst for victory as well as enthusiasm, a strong work ethic and tenacity; key elements for all the Scuderia members to write together a new winning chapter in the history of Ferrari."
Vettel described his move to Ferrari as the realisation of a long-held ambition, inspired by the exploits of another German multiple champion who won five of his seven world titles with the team.
"The next stage of my Formula One career will be spent with Scuderia Ferrari and for me that means the dream of a lifetime has come true," Vettel explained.
"When I was a kid, Michael Schumacher in the red car was my greatest idol and now it's an incredible honour to finally get the chance to drive a Ferrari. I already got a small taste of what the Ferrari spirit means, when I took my first win at Monza in 2008, with an engine from the Prancing Horse built in Maranello.
"The Scuderia has a great tradition in this sport and I am extremely motivated to help the team get back to the top. I will put my heart and soul into making it happen."
Vettel has been the dominant force in Formula One racing ever since joining Red Bull ahead of the 2009 season. He claimed four consecutive drivers' crowns between 2010 and 2013, and scored a total of 38 Grand Prix wins and 44 pole positions over his six years with the team.