Costa, a former scout for Scottish Champions Celtic, has worked extensively in the Middle East, including coaching the Qatar womens team and, since 2012, the Iran women’s team.
The 36-year-old, who has also coached Benfica’s male youth teams will join Clermont officially at the end of the season.
“It should help the club enter a new era,” the French Ligue 2 club said.
Before Costa, the highest-profile appointment of a woman as coach of a men’s team in Europe was that of Carolina Morace, who took charge of Italian Serie C1 team Viterbese for two matches in 1999.
Costa, who scouted for Celtic between 2008 and 2011, has also managed Portuguese lower-league men’s team Cheleirense.
She is a highly coach having taken her UEFA ‘A’ qualification with eth Portuguese FA and has a Sports Science degree and a Masters.
At Clermont, she will replace former Montpellier midfielder Regis Brouard, whose contract as head coach expires at the end of the season.
The club are 14th in the French second-tier with two matches to play.