He had been under pressure to step down and his resignation came at the end of a week where Hermoso filed a legal complaint against him.
A prosecutor also filed a complaint with Spain’s high court against Rubiales for sexual assault and coercion.
Victor Francos, Spain’s secretary of sport and head of the state-run National Sports Council, said: “It has not ended here, now is when it really begins. We have to learn from what has happened.
“This situation is going to have an impact on how we see the behaviour and functioning of the federations as a whole, not just the football one.”
Rubiales, who has also resigned from his role as vice president with UEFA, remains under investigation by FIFA, who have suspended him from all football-related activity for 90 days.
Rubiales announced his resignation during an interview with Piers Morgan, due to be broadcast on Monday.
He explained he came to his decision after speaking with his father and daughters.
Rubiales added in an open letter that he hoped his departure would mean Spain’s joint bid with Morocco and Portugal to host the 2030 World Cup could remain on track.