“In this strange time, when truth is too often dismissed as ‘fake news,’ we as publishers prefer to give voice to a respected artist, rather than bow to those determined to silence him,” she said in a statement. “We firmly believe in upholding the right to freedom of speech in the world of publishing and, as a result, we’re pleased to support not only this terrific book but also — and even more importantly — this democratic principle.”

Arcade is an imprint of the independent publisher Skyhorse, a company that has been willing to court controversy in the past, with provocative authors like the attorney and commentator Alan Dershowitz, a frequent defender of Donald J. Trump, and the conspiracy theorist Jim Garrison.

At a moment when publishers are increasingly wary of sparking controversy and driving a social media backlash, Arcade’s decision to publish Mr. Allen caught some in the industry by surprise, particularly after Hachette’s rapid about face.

Grand Central had acquired the rights to Mr. Allen’s autobiography in March 2019, but had only announced that fact earlier this month. The journalist Ronan Farrow, whose best-selling book “Catch and Kill” had been released by Little, Brown, another Hachette imprint, last year, quickly lashed out at the company, saying it had secretly planned to publish Mr. Allen’s book behind his back, and that he would no longer work with the publisher.

Mr. Farrow, whose reporting on accusations of sexual assault against Harvey Weinstein and other powerful men helped touch off the #MeToo movement, is Mr. Allen’s son with the actress Mia Farrow. Mr. Farrow and his adopted sister, Dylan Farrow, have long accused Mr. Allen of molesting her when she was a child, allegations he has denied. Mr. Allen was not charged after two investigations.

“Your policy of editorial independence among your imprints does not relieve you of your moral and professional obligations as the publisher of ‘Catch and Kill,’ and as the leader of a company being asked to assist in efforts by abusive men to whitewash their crimes,” Mr. Farrow wrote to Michael Pietsch, the chief executive of Hachette.

Mr. Pietsch had defended the decision to publish Mr. Allen’s book, but a staged walkout of more than 100 employees was part of the pressure that led to the reversal of the plan.