O'Leary made the comments earlier this month during a press conference, where he was asked whether he believed the language he had used to describe competitors was appropriate.
Rather than retracting the remark at the time, O'Leary doubled down, saying he would "happily offend" rival airlines.
The comments prompted the Dublin Rape Crisis Centre (DRCC) to write to the Ryanair boss, asking him to apologise. The organisation said the language risked trivialising the serious nature of rape and its impact on victims and survivors.
Initially, O'Leary rejected the request. In his response to the DRCC, he said: "Since I clearly did not trivialise the heinous crime of rape, I will certainly not be issuing an apology or accepting your offer of training."
However, O'Leary has since changed his position and issued a public apology in a video posted on Friday.
The Ryanair chief said that conversations with family and friends, both inside and outside the airline, had led him to reconsider his choice of words.
"I have come to realise however that the word that I used so carelessly has caused considerable upset and offence to a wide number of people, especially to victims and survivors," he said.
"I want to apologise, sincerely and unreservedly, to those people, especially to the survivors."
The Dublin Rape Crisis Centre has welcomed the apology and reiterated its offer to provide O'Leary with training on the impact of sexual violence.
The organisation also said it hoped the public apology would help raise awareness of the harm that can be caused when issues such as sexual violence are trivialised.
O'Leary's apology marks a reversal from his initial refusal to withdraw the comments, following criticism from organisations concerned about the impact of his language on victims and survivors of sexual violence.
