Last month, Lyon was demoted to the second-tier Ligue 2 by the financial regulator of French football, which had imposed budgetary restrictions on the club in November.
American entrepreneur Michele Kang subsequently took over as club president from her fellow countryman John Textor.
The FFF stated that Lyon must reduce its wage bill and transfer budget for the upcoming season.
"Lyon wishes to express gratitude to the appeals commission for recognizing the ambitions of the club's new management," the club remarked in a statement.
"Today's ruling marks the initial step towards rebuilding trust in Lyon."
Two weeks ago, Textor announced he would step back from the club's daily operations.
Kang, who is the second-largest shareholder behind Textor, was already serving as the president of the Lyon women's team.
Lyon finished sixth in Ligue 1 last season, qualifying for the Europa League, and will be allowed to participate in that competition following the successful appeal, although they had already agreed to pay a fine to UEFA.
Textor became Lyon's majority owner in December 2022, succeeding long-time president Jean-Michel Aulas, who had led the club to unprecedented success.
Under Aulas, Lyon won seven consecutive French titles from 2002 to 2008.

Textor, 59, also has stakes in the Brazilian club Botafogo and the Belgian club Molenbeek.
He sold his 43 percent stake in the Premier League team Crystal Palace in mid-June as he attempted to stabilize the finances at Lyon.
Lyon has reduced its salary expenses by releasing forward Alexandre Lacazette and goalkeeper Anthony Lopes from the squad.
They have transferred Rayan Cherki to Manchester City and Maxence Caqueret to Como.
Textor mentioned that his Eagle group has invested an additional 83 million euros into the club.
Only five clubs have won Ligue 1 more times. Paris Saint-Germain holds the record with 13 titles.
Lyon commenced their pre-season training on Monday. Their first match of the Ligue 1 season will be against Lens during the weekend of August 15-17.