The ladies who lunch are booking a table in New York.

The gender-bending revival of Stephen Sondheim’s “Company,” which won rave reviews in London, will open on Broadway next fall, several theater sources told The Post.

Directed by Marianne Elliott, the whiz behind the Tony-winning “War Horse,” “The Curious Incident of the Dog in the Night-Time” and last season’s revival of “Angels in America,” “Company” just extended its run in London until March.

The twist here is that Bobby, the bachelor at the center of the show, is now Bobbie, a bachelorette, brilliantly played by Rosalie Craig. Although celebrated in London, she’s yet to make her Broadway debut. But she will next fall, in “Company,” leading a cast that includes Patti LuPone, who stops the show with her rendition of “The Ladies Who Lunch.”

LuPone has done something only she could do: upstage Elaine Stritch, who originated the role and made that song her calling card. But that shouldn’t surprise anyone who caught LuPone in John Doyle’s 2005 revival of “Sweeney Todd.”

I didn’t think anyone could match Angela Lansbury as Mrs. Lovett. Then LuPone came out with her tuba — all the actors played instruments in that production — and walked off with a Tony nomination.

LuPone has said that she’s through with musicals. She was exhausted after “War Paint,” valiantly struggling through the run with a bad hip (she had it replaced after the show closed). But she’s enjoyed working with Elliott, and will reprise the role in New York.

LuPone has two Tonys: one for “Evita,” the other for the 2008 revival of “Gypsy.” There’s a third in her future for “Company.”

Sondheim kept an eye on this revival, sources say, just to make sure the gender switch didn’t radically alter the tone and style of the show. He took a break from his new musical, based on the Luis Buñuel movies “The Discreet Charm of the Bourgeoisie” and “The Exterminating Angel,” to attend “Company” rehearsals in London. He suggested some changes and is said to be delighted to see it come to Broadway.

A few critics have complained that this revival, which is set in the present, doesn’t quite capture the spirit of New York. That is a problem since “Company,” originally set in 1970, is the essence of sophisticated New York. But Elliott, sources say, is taking the criticisms into account and will inject more of the Big Apple into the Broadway production.

I expect to see her huddled over her notes at the Grill in the Seagram Building, which represents the New York at the heart of “Company.”

Disgraced impresario Garth Drabinsky returned to Broadway this week for the first time since he got out of jail in Canada five years ago.

Drabinsky, once one of the most powerful producers in New York, attended a performance of Harvey Fierstein’s “Torch Song.” Its director, Moisés Kaufman, is developing a new show for Drabinsky based on the songs of Stephen Foster.

Drabinsky was convicted of fraud and forgery in 2009 in Canada for his part in the collapse of his company Livent, the producer of “Ragtime” and “Kiss of the Spider Woman.” Drabinsky was under indictment in the United States, but all charges against him were dismissed this past summer, so he can now enter the country without getting arrested.

But I wonder if he can still get a good table at Joe Allen.

You can hear Michael Riedel weekdays on “Len Berman and Michael Riedel in the Morning” on WOR radio 710.