Vice Media — the Brooklyn-based gonzo news empire founded by Shane Smith — has bought Refinery29, a lifestyle site that caters to millennial women.

Terms were not disclosed, but sources familiar with the matter said the deal was mostly stock, valuing Refinery29 at about $400 million, and that it values the combined online publishers at about $4 billion.

The deal, which has been rumored since the summer, has been met with some skepticism.

“The cultures are oil and water. Misogyny meets feminism,” a digital executive told The Post. “When they merge, there will be very deep cuts on the Refinery side,” predicted the executive. “Vice will gut them.”

Vice, once valued at a whopping $5.7 billion, has already tried and failed to make a grab for female consumers with Broadly, a female-centric site that folded earlier this year.

Still, Vice said Wednesday it believes that Refinery29, which was once valued at $500 million, will help it grow its footprint. That’s despite the fact that Vice Chief Executive Nancy Dubuc has been slashing costs since she joined the company last year.

Vice says it will be profitable by early 2020. Refinery 29’s co-founders and co-CEOs Philippe von Borries and Justin Stefano, will stay on and report directly to Dubuc.

Vice Media is estimated to have revenue of more than $600 million. Close to 60 percent of its digital traffic of 300 million monthly visitors comes from overseas. Refinery29 revenue was estimated to be around $100 million, and most of its traffic comes from US-based consumers.

Dubuc, who replaced Smith as CEO, called the deal “an expansive moment for independent media,” and added that the companies will “not allow a rapidly consolidating media ecosystem to constrict young people’s choices or their ability to freely express themselves about the things they care about most.”

Her sentiment breezed past the fact that Refinery29 and Vice, which targets mainly young millennial men, are the latest victims of the digital media consolidation.

Last week, one-time digital media darling Vox Media scooped up New York Media, the firm behind sites Vulture and The Cut, as well as New York Magazine.

This February, Dubuc said Vice would slash 10 percent of its workforce or 250 jobs across all departments, as Vice lost its weekly documentary show on HBO, as well as its half-hour news show, “Vice News Tonight.”

In a much-needed cash infusion, Vice Media took on $250 million in debt financing from a group of investors that includes Soros Fund Management, 23 Capital, Monroe Capital and Fortress Investment Group in May. The funds are intended to push the company toward a sustainable future.

In 2017, Vice settled four sexual harassment or defamation lawsuits filed by female employees — one against the then-president — and this year, the company ponied up $1.87 million to settle a class-action lawsuit claiming the company underpaid its women workers.