In a statement the association confirmed Gamel quit last week citing personal reasons.
Fiji Football president Rajesh Patel praised Gamel for lifting the country's FIFA world ranking from 189 to 163.
Patel said Gamel's last outing with the national teams was for the Pacific Games campaign in July which saw bronze medal finishes for both the Fiji men's and women's teams.
Goalkeeper coach Xavier Henneusse, who was brought in by Christophe Gamel, will also be leaving with Gamel at the end of the month.
