Reese Witherspoon’s media business, Hello Sunshine, is selling itself to a firm backed by private-equity giant Blackstone Group Inc., the companies said, part of a plan to build an independent entertainment company for Hollywood’s streaming era.

The companies didn’t disclose the terms of the deal. People familiar with the matter said it values Ms. Witherspoon’s company, whose production slate has included programming such as the HBO drama “Big Little Lies,” at about $900 million.

The as-yet-unnamed media venture Blackstone is backing will be run by former Walt Disney Co. executives Kevin Mayer and Tom Staggs. Hello Sunshine will be its first acquisition. Ms. Witherspoon and Hello Sunshine Chief Executive Sarah Harden will join the board of the new company and will continue to operate Hello Sunshine.

Blackstone is spending more than $500 million in cash to purchase shares from existing Hello Sunshine investors, including AT&T Inc. and Emerson Collective, some of the people familiar with the matter said. Ms. Witherspoon and some Hello Sunshine executives and investors will roll over the remaining equity into ownership stakes in the new company Blackstone is forming.

Ms. Witherspoon, the actress and entrepreneur who founded Hello Sunshine in 2016, said in an interview that the deal is a major endorsement of her bet that Hollywood needs more stories told by and for women. Other Hello Sunshine titles include Hulu’s “Little Fires Everywhere” and Apple Inc.’s “The Morning Show.”

“I’m going to double down on that mission to hire more female creators from all walks of life and showcase their experiences,” Ms. Witherspoon said. “This is a meaningful move in the world because it really means that women’s stories matter.”

Messrs. Mayer and Staggs are hunting for content companies amid a land-grab for high-quality programming in Hollywood. Streaming services—from incumbents such as Netflix Inc. to new services launched by traditional giants—are trying to feed their platforms with as much premium TV and movie content as possible.

Amazon.com Inc. recently agreed to purchase the studio MGM Holdings for $8.45 billion including debt, and SpringHill Co., the firm founded by LeBron James, is exploring a sale seeking a valuation of $750 million, according to a person familiar with the matter.

The Blackstone-backed company is separate from a special-purpose acquisition company Mr. Staggs runs with Mr. Mayer. The two executives have scoped out deals with other firms including Westbrook Inc., the media company co-founded by Will Smith and Jada Pinkett-Smith.

The changes in streaming-driven Hollywood are having an impact on the business of creating programming. As major studios direct movies and shows to their own streaming platforms, that can sometimes put them in conflict with actors and producers who want to ensure that the value of their work is being maximized. That was illustrated last week when Scarlett Johansson filed suit against Walt Disney Co. over the Marvel movie “Black Widow,” saying the company violated her contract by releasing the film on Disney+ at the same time it went to theaters.

Mr. Mayer said that the new company, like Hello Sunshine, will be free to license programs to any studio or network, giving it an edge over major studios that must feed their own streaming services.

“The big guys aren’t licensing their content outside of their own closed walled gardens,” Mr. Mayer said. “And that’s where a scaled, independent entity like ours can really have an advantage in the marketplace.”

The value that the new Blackstone-backed company will get from Hello Sunshine’s past titles will vary. For example, Hello Sunshine co-owns titles such as “Little Fires Everywhere,” and retains the right to sell them to other distributors after initial licenses expire, some people familiar with the deal said. For some other shows, such as “Big Little Lies” and “The Morning Show,” Hello Sunshine serves as a producer, but doesn’t retain co-ownership.

The new company would have an ownership interest in any fresh programming from Ms. Witherspoon’s company. Hello Sunshine, which will be profitable this year, also has a kids and animation division with a coming slate that includes four projects with four different streaming services, according to people familiar with the matter.

Hello Sunshine also operates Reese’s Book Club, which curates titles for readers and holds events for members. The company’s relationship with authors helps when its executives are bidding for the rights to turn books into shows and movies, Ms. Harden said. “The advantage that we have is in tentpoling a book and putting a spotlight on it,” she said.

For Blackstone, which is financing the media venture through its main private-equity fund, the deal is an example of the thematic investing style the firm has embraced in recent years. Developing theses about the way the world is heading and finding ways to put money to work that benefit from those trends has led it to plow billions of dollars into fast-growing companies.

“We’ve had among our highest conviction investment themes the continued and long-dated demand for high quality content,” said Joseph Baratta, Blackstone’s global head of private equity.

The firm’s real-estate business is a major owner of offices and studio space in Burbank and Hollywood. It announced a deal Sunday to develop new film and TV studios in the U.K. in partnership with Hudson Pacific Properties Inc.

Blackstone also owns music-rights organization Sesac Performing Rights LLC through its long-term private-equity fund, and in March it said it would invest in royalty-free music platform Epidemic Sound through its growth fund.

Write to Benjamin Mullin at Benjamin.Mullin@wsj.com and Miriam Gottfried at Miriam.Gottfried@wsj.com