Costa hit the headlines last month when she was handed the reins at Clermont, giving her the opportunity to coach at a higher level than any other woman in European men's football.
However, the 36-year-old has now opted against taking charge of the French side, much to the surprise of Clermont president Claude Michy.
In a statement on the club's official website, Michy said: "Helena Costa decided not to honour her commitments ... (and will) therefore not assume the (role of) coach for the coming season.
"This decision was sudden and surprising.
"I deeply regret this situation. I thank all of those who have supported me and I am most grateful."
Clermont have not revealed the reasons behind Costa's decision.
‘Ruben is no miracle-maker. This year will be complicated and fans need to be patient, but he’s a perfectionist. He’s amazing at understanding players’ minds’: Manchester United manager will need time to implement ideas, says Amorim's former player
‘Planting that flag at Fenerbahce wasn’t premeditated. It just happened. I had tried to pass it on, but ended up with a place in Turkish footballing folklore’: Graeme Souness recounts infamous act as Galatasaray manager in 1996
