The 1981 world rally champion and former Dakar winner, 57, said his decision is backed by "requests from many FIA member clubs".
It is believed two of the supportive clubs are the influential AAA of America, and Germany's ADAC.
"I think the time has come for a change," said Vatanen.
It is not clear if Vatanen, who last month was not re-elected to the European Parliament, will face off against Mosley in the late October elections, or whether the controversial incumbent will instead step down.
The Finn said: "My main focus is to reconcile views within the FIA and bring transparency to its stakeholders."