"Jean Todt has been elected president of the FIA for a four-year term by the FIA General Assembly at its annual meeting in Paris," an FIA statement said.
The 63-year-old Frenchman won 135 votes to 49 for Vatanen, the former world rally champion who was his sole rival for the most powerful position in world motorsport. There were 12 abstentions.
"It’s positive, very positive," retired Formula One champion Michael Schumacher, who won five of his seven titles with Todt at the Italian glamour team, told reporters after the news was announced.
Todt had been backed throughout an increasingly acrimonious campaign by Mosley, who will remain in the FIA senate, and had also received support from Formula One supremo Bernie Ecclestone.
Vatanen, a former European parliamentarian, stood on a platform of change and transparent governance to make a clean break from the controversial Mosley era.
Mosley, whose private life became very public last year when it emerged that he had engaged in sado-masochistic sex sessions with prostitutes, had been FIA president since he ousted Frenchman Jean-Marie Balestre in 1993.
Formula One teams, who had clashed repeatedly with Mosley earlier in the year while threatening a breakaway series, welcomed the appointment of a man many had previously expressed misgivings about.
"I would like to send my best wishes to Jean Todt in his new role, as I have always appreciated his ability, dedication and commitment," said Ferrari president Luca di Montezemolo in a statement issued by the Formula One Teams Association (FOTA).
"I am sure that, under his guidance, the Federation will be rejuvenated and will restore a climate open to dialogue and constructive collaboration with the teams and FOTA, thus ensuring stability of the regulations and the whole environment," added Todt’s former boss.
"Formula One is about to embark on a new phase," said Montezemolo, who is also chairman of FOTA.
"All the stakeholders must work together with an eye to the future, to increase the credibility and interest generated by this sport, tackling the technical and environmental challenges that await it while keeping unchanged those characteristics that have made it one of the most popular (sports)."