Sarah Forsyth won her case for unfair dismissal against the famous public school last July. During the tribunal hearings, she alleged that she helped Harry to cheat in his A-Level artwork - a claim that was rejected by Clarence House.
A statement issued on behalf of both Eton and Ms Forsyth said: "Ms Forsyth and Eton College have reached agreement on a settlement acceptable to both parties, and the proceedings between them are now concluded." It is understood that Ms Forsyth receives 45,000 under the settlement. She is understood to be paying about 15,000 to her lawyers.
Ms Forsyth claimed she had been sacked unfairly after being bullied.
But despite winning her case, she was criticised by the employment tribunal for abusing her position when she made a secret tape-recording of Prince Harry.
Eton College was also criticised over procedures at the school.
The prince was drawn into the dispute because of a short encounter with Ms Forsyth in the summer of 2002, when he was making final preparations on his AS-Level art coursework.
She made a secret tape-recording of a conversation with him on his way to his final exam. Ms Forsyth argued that the tape backed up her claims that she had effectively written most of the text of the prince's "expressive journal" - a written piece to accompany his art coursework.
The tribunal, which met in Reading, Berkshire, found that Ms Forsyth had been bullied and undermined by her head of department, Ian Burke. It also ruled that the decision not to renew her temporary contract was not handled "independently" by the headmaster, Anthony Little.
But her version of her claims involving the prince was "muddled" and her secret taping of a conversation with him was "clearly an abuse of the position of trust in the pupil-teacher relationship".
Ms Forsyth's lawyer, Anthony Sakrouge, said: "She is content that the settlement that has been agreed reflects the fact that she was unfairly treated."
An additional statement from Eton said: "The college is pleased that it has reached a satisfactory settlement. Given that the college had successfully defended at tribunal her more extreme allegations of whistleblowing, sex discrimination and cheating, we felt it was sensible to bring this matter to a close in relation to the remaining unfair dismissal element of her claim."
But last year, after the tribunal ruled that Ms Forsyth's dismissal was unfair, Eton insisted she should get no compensation, "as she would have been summarily dismissed for gross misconduct for secretly tape-recording a conversation she had with a pupil".
The prince left Eton with a B in art and a D in geography. He was cleared of cheating after an investigation by the examinations board, Edexcel, found no evidence. Had he been found guilty, he would have failed to get the exam results needed to follow his career in the military.
Last night, the Royals refused to become embroiled in more controversy. A Clarence House spokesman said: "It was a dispute between Ms Forsyth and Eton. We have no comment to make."