The woman, who is now 41, had taken a civil action against the man over the abuse, which happened over seven years between 1982 and 1989 when she was between 12 and 19 years old.
The man denied all the allegations and his lawyers tried to stop her taking the case because of the delay in bringing proceedings.
However, the High Court judge found that she should not be prevented from taking the action.
He ruled she had suffered a severe psychological injury as a result of the abuse, which had affected her ability to take the case.
The court had heard that she is suffering from severe post traumatic stress disorder.
It is believed to be the first time this issue has ever been fought and decided in court.
In making the award, the judge said it was difficult to overstate the profound and lasting effects of prolonged sexual abuse on a person whose childhood was blighted by this conduct.
Neither the man nor the woman can be named until further submissions are made in court on Friday.
The man was charged with 24 counts of indecent assault but two trials ended with the jury being unable to agree a verdict.
After the second trial, the State decided not to pursue the prosecution any further.
Mr Justice Sean Ryan ruled the woman had established on the balance of probabilities that the man had carried out acts of sexual abuse against her.
He said her evidence was coherent, consistent, and credible and her account was detailed and candid. He ruled that the man’s evidence was inconsistent and unconvincing.
The judge said the man’s proposition that she had concocted the case to get back at the man for spurning her advances was wholly unconvincing and did not accord with logic or with her behaviour.
The court heard that what had led to her taking the action against the teacher was the realisation that other girls might be at risk.
Two other former dancing students of the man gave evidence on the woman’s behalf. One said that he would hug and kiss students when they went up to give him money after the class.
This made them so uncomfortable that they made an arrangement to take turns so that only one girl would have to go up each week and they would give all the money to her. She also outlined a number of other incidents.
The second student described how the man had stopped his car in a lay-by when she was alone with him and had tried to kiss her.
She also described another incident in which he put his hands on her and said she changed dancing school after that.