The 78-year-old "Blue Jasmine" writer-director's essay will be published in Sunday's newspaper.
His daughter Dylan Farrow, 28, posted a letter on the Times' website last weekend, disclosing harrowing details about what she says was Allen's repeated sexual abuse of her as a child.
While Farrow's brother Ronan and mother Mia have publicly supported Farrow's decision to tell her story, another brother Moses said he believes the allegations are the result of Mia turning her children against Allen because he left Mia for her adopted 19-year-old daughter, Soon-Yi Previn, in 1992. Allen has always emphatically denied the abuse claims.
"Of course, I did not molest Dylan," Allen emphasized in the Times article to be published Sunday. "I loved her and hope one day she will grasp how she has been cheated out of having a loving father and exploited by a mother more interested in her own festering anger than her daughter's well-being."
Allen echoed his lawyer's statement from earlier this week that the allegations were implanted in Farrow's mind by her mother during what the filmmaker categorized as a "terribly acrimonious breakup."
"The self-serving transparency of her malevolence seemed so obvious I didn't even hire a lawyer to defend myself," he wrote about Mia.
"I naively thought the accusation would be dismissed out of hand because, of course, I hadn't molested Dylan and any rational person would see the ploy for what it was," he said. "Not that I doubt Dylan hasn't come to believe she's been molested, but if from the age of 7 a vulnerable child is taught by a strong mother to hate her father because he is a monster who abused her, is it so inconceivable that after many years of this indoctrination the image of me Mia wanted to establish had taken root? ... This piece will be my final word on this entire matter and no one will be responding on my behalf to any further comments on it by any party. Enough people have been hurt."
2014: The Year in Music [PHOTOS]