Roseanne Barr may be finished, but the Conners are not.

Less than a month after ABC canceled the hit revival of “Roseanne” because of a racist tweet by Ms. Barr, the network has decided to go forward with a spinoff that will not include her. ABC said that Ms. Barr would not receive any payment from the network for the series, which is tentatively titled “The Conners.”

The spinoff, scheduled to air on ABC in the fall, will include the principal “Roseanne” cast members John Goodman, Laurie Metcalf and Sara Gilbert. The producers who ran “Roseanne,” including Tom Werner of Werner Entertainment, and the show’s writing staff will also return. The new anchor of the Conner family is expected to be Darlene, the Roseanne character’s younger daughter, who is played by Ms. Gilbert. The season will be 10 episodes.

Before ABC approved the spinoff, Ms. Barr and Werner Entertainment agreed on a financial settlement, according to a person briefed on recent discussions, who spoke on the condition of anonymity to describe negotiations that took place among the star, producers and executives. That person would not reveal the sum of the payment.

In a statement on Thursday, Ms. Barr said, “I regret the circumstances that have caused me to be removed from ‘Roseanne.’ I agreed to the settlement in order that 200 jobs of beloved cast and crew could be saved, and I wish the best for everyone involved.”

ABC canceled “Roseanne” on May 29, hours after Ms. Barr used her Twitter account to liken Valerie Jarrett, a former special adviser to President Barack Obama who is African-American, to the offspring of the Muslim Brotherhood and “Planet of the Apes.”

How the new show’s writers will explain the absence of the Conner family matriarch remains an open question, but a description included as part of an ABC press statement on Thursday referred to “a sudden turn of events” that forces the Conners to “face the daily struggles of life in Lanford in a way they never have before.”

“Roseanne” was a critical and commercial success for ABC during its original incarnation from 1988 to 1997. The reboot premiered on the network on March 27. It was born of a strategy hatched by ABC executives during a meeting at the network’s Burbank headquarters on the day after Donald J. Trump won the 2016 presidential election.

Channing Dungey, the president of ABC Entertainment, described ABC’s thinking in an interview with The New York Times published two days after the “Roseanne” premiere. “We had spent a lot of time looking for diverse voices in terms of people of color and people from different religions and even people with a different perspective on gender,” she said. “But we had not been thinking nearly enough about economic diversity and some of the other cultural divisions within our own country.”

The ratings for “Roseanne” surprised ABC executives, who said the size of the audience was more than twice what they had expected. President Trump was enthralled by the ratings numbers and made a congratulatory call to the show’s star.

Even before Ms. Barr attacked Ms. Jarrett, her use of Twitter was a subject of concern for the network and others in the star’s orbit. Months before the rebooted version of the show aired, during an interview at a conference for television critics in Pasadena, Calif., Ms. Barr said her children had locked her Twitter account. “I didn’t want it to overshadow the show,” she said.

After the revived sitcom had proved a hit, she continued tweeting, however, often publicizing various conspiracy theories.

Despite the show’s popularity, it generated controversy, partly because of Ms. Barr’s vocal support — in real life and through her Roseanne Conner character — for Mr. Trump. The show itself drew scrutiny for plot points and punch lines, especially with its third episode, which featured a glib exchange between Roseanne and her husband. After waking up in front of the TV, Dan Conner says, “We missed all the shows about black and Asian families.” To laughter from the studio audience, Roseanne responds: “They’re just like us. There, now you’re all caught up.”

The executives and producers watching over the series repeatedly defended it, arguing that “Roseanne” gave voice to the kind of working-class family often overlooked by Hollywood.

After Ms. Barr’s racist tweet, Ms. Dungey and her fellow ABC executives acted swiftly. Ms. Dungey, the first black president of a television network, was joined in the decision to cancel the show by Ben Sherwood, the president of the Disney-ABC Television Group, and Robert A. Iger, the chief executive of ABC’s parent company, the Walt Disney Company.

ABC’s approval of a Roseanne-less version of the show started with “Roseanne” producers making their pitch to the network’s executives. Two questions came up during discussions: Would Ms. Barr herself receive compensation for a “Roseanne” spinoff? And would there be blowback from those viewers who were glad that the network had canceled “Roseanne,” not to mention from the stars and producers of other ABC programs?

Examining the genesis of the original “Roseanne,” the executives and producers believed they had found a way to move forward without ABC’s paying Ms. Barr. Although she has been credited with coming up with and shaping the Roseanne Conner character, the creation of the show itself is credited to Matt Williams, a writer-producer who was fired after clashing with the star early in its run.

When “Roseanne” was canceled last month, many television executives expressed doubt that even entertaining the idea of a spinoff was possible. Marcy Carsey, one of the show’s founding producers, recently said she would not try to continue with a similar series.

“I think I would just say, ‘O.K., we had a wonderful run,’” Ms. Carsey said at a television festival in Austin, Tex., this month.

Ms. Carsey’s former producing partner, Mr. Werner, held a different view. “We are grateful to have reached this agreement to keep our team working as we continue to explore stories of the Conner family,” he said in a statement.

By going ahead with the spinoff, ABC executives are gambling that viewers will approve of the network’s decision to bring back the Conners and will display an interest in characters who once served as foils to the lead.

A recent Quinnipiac University National Poll found that 48 percent of registered voters agreed with ABC’s decision to cancel the show, and 34 percent said they would have preferred to see it remain on the air. Among those identifying themselves as Republican, 50 percent disagreed with the network’s move.

Other notable shows — like “House of Cards,” “Transparent” and “Two and a Half Men” — have continued without key cast members. And there is precedent for continuing a series without its eponymous star. The 1980s sitcom “Valerie” was retitled “Valerie’s Family: The Hogans” and then “The Hogan Family” after Valerie Harper left during the show’s second season because of a salary dispute. The writers killed off Ms. Harper’s character — it was a car crash — and brought aboard Sandy Duncan as “Aunt Sandy,” the show’s new matriarch.

A version of this article appears in print on , on Page B1 of the New York edition with the headline: ABC Plans ‘Roseanne’ Spinoff, Without Barr. Order Reprints | Today’s Paper | Subscribe