The film director denied sexual assault on Dylan Farrow, who lost in 1992.
Allen's lawsuit stated that the study was aware of the accusations he had received several decades ago - and that the authorities had concluded that there was not enough evidence against him - and that they owed him 68 million in guaranteed payments in the agreement they had sealed.
Amazon shelved the release of "A Rainy Day in New York" in 2018, and then abandon a deal for three more movies.
The four-time Oscar victor reportedly expressed sympathy for disgraced movie producer Harvey Weinstein, and later accused his adopted daughter of "cynically using the #MeToo movement" to reiterate her claims.
Allen said Amazon pulled out because of long-standing allegations that he molested his adoptive daughter Dylan Farrow when she was seven years old.
In an interview with Argentinean broadcaster Eltrece, Allen said he "should be the poster boy for the Me Too movement" since he had worked with "hundreds of actresses" and was "only accused by one woman in a child custody case".
In Amazon they made a decision to disregard their agreement with Woody Allen for the resurgence of accusations towards the director by Mia Farrow.
Klieger said that Allen's remarks hurt the project, which starred Timothée Chalamet, Selena Gomez, Elle Fanning, Jude Law and Rebecca Hall, and made the film too hard to promote.
"A Rainy Day in New York" was released this fall outside the United States by his production company Gravier Productions.