The letter addresses a number of areas of concern for pilots including pay, conditions, rosters and comments made by Mr O'Leary at the company's AGM.
The operating chief, who assumed the post in 2014, has been at the airline since 1988, joining as an engineer and rising to direct the department.
In a three-page letter O'Leary apologises for the changes that caused problems with the rota and said he would beat any deal offered to any of its 4,200 pilots by other airlines, if they remained loyal.
Mr Hickey was in charge of pilot rotas when the disruptions began last month and did not have enough standby pilots to ensure the airline could operate properly, leading to the cancellation of more than 2,000 flights.
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Mr O'Leary's apology came after he accused the pilots of being "full of their own self-importance".
The letter also received a lukewarm response from pilots who contacted the BBC. While Ryanair does not recognize trade unions, pilots have launched web and social media forums in recent months to air their grievances.
But in the letter he urges pilots to stay with Ryanair "for a brighter future".
In his role, Mr Hickey was responsible for scheduling shifts for pilots.
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He also offers pilots a bonus of €12,000 (£10,700) and promises he will exceed the pay deals offered by rival airlines.
The company was already under heavy fire for cancelling up to 50 flights a day in the middle of September before an additional 18,000 flights were axed at the end of the month.
More than 700,000 passengers' travel plans have been affected by what Ryanair boss Michael O'Leary admitted was a "cock up".
Michael Hickey will leave his post from the end of October after a 30-year career with the airline.
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But passengers have complained about the short notice of the cancellations and the consumer group Which? said Ryanair's compensation information was "woefully short".