Corinne Diacre, 39, former captain of the France women's team, has signed a two-year deal to take over.
"Corinne Diacre has accepted the position of coach of Clermont Foot ... and will take up the post early next week," the club said on their website (www.clermontfoot.com) on Saturday.
Costa, who last month became the first female to be appointed coach of a men's team in the top two divisions of European football, quit before taking charge of Clermont.
The 36-year-old had previously coached the Iran women's team and scouted for Scottish Premier League club Celtic.
Portuguese Costa resigned because she said she found out players were being hired at Clermont without her consent.
No woman had come as close as Costa to coaching a top men's professional team in Europe but that task now falls to Diacre.
Carolina Morace was appointed coach of Serie C1 (third division) club Viterbese in Italy in 1999. She resigned after two matches, citing media pressure.
AS Roma have had two women chairpersons, Rosella Sensi and Flora Viola, and Gisela Oeri was president of Swiss club Basel for five years from 2006.
In the late 1990s and early 2000s, France picked Nelly Viennot as the first woman to be assistant referee in an elite match.
Viennot also served as assistant referee in Champions League games.
Referee Bibiana Steinhaus officiates in German second division games. She is the first female referee in Bundesliga 2 and the first to have been a referee in the German Cup.
Maria Jose Claramunt is the director of Spain's national team, responsible more for marketing than sporting issues, while Karren Brady is vice-chairman of English Premier League West Ham United.
(Writing by Tony Jimenez, editing by Pritha Sarkar)
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