Her departure removes a lightning rod for Republican critics as Obama and his Democrats try to retain control of the U.S. Senate in November midterm elections, where problems with Obamacare reforms will be a top issue.
The October 1 launch of the new Obamacare health insurance marketplace, which was plagued by computer problems, has been condemned by Republicans as a step toward socialized medicine.
Obama has chosen Sylvia Mathews Burwell, his budget director, to replace Sebelius, the official said. She will manage the continued implementation of the Affordable Care Act, the signature legislation of Obama's two terms as president.
Obama was due to announce the change with Sebelius and Burwell at his side at a White House event at 10:45 a.m. EDT (1445 GMT) on Friday.
Sebelius, 65, became the public face for the problem-plagued start to the enrollment period for Obamacare, which was meant to reduce the number of Americans without health insurance and cut into massive U.S. healthcare costs.
When enrollment opened in October, a website used to shop for insurance in 36 states, HealthCare.gov, failed to work for weeks.
Even as she took responsibility for the failures, Obama stuck by Sebelius, brushing aside pressure to fire her.
"Hold me accountable for the debacle. I'm responsible," Sebelius said at an October 30 hearing.
Burwell, a former official at the Gates Foundation and Wal-Mart Foundation, helped the administration manage its response to a shutdown of the federal government brought on by a budget battle with Republicans in October. She also was a key player in talks that yielded a two-year budget agreement in December.
"The president sought a nominee with strong credentials in management, implementation and performance for this important role," the official said, noting she was confirmed unanimously to lead the budget office less than a year ago.
One of the first challenges for Burwell will be to work with health insurers in the coming months as they set prices for Obamacare plans in 2015. Industry executives have warned that many states could see double-digit increases in monthly premiums as they try to account for the higher proportion of older policyholders who often cost more to cover. Such price hikes would provide fodder for Republican opponents of the law who say it creates financial burdens for individuals and businesses.
Lamar Alexander, the top Republican on the Senate health committee, called the move "the right decision," but made it clear that the switch would not mean an end to Republican pressure on the law.
"The challenge for Ms. Burwell, or any other successor, is to help Congress find the right way to repair the damage Obamacare has done to American families," Alexander said in a statement.
Sebelius continued to bear the brunt of criticism from Congress, where she testified as recently as Thursday, giving no sign that she was about to step down.
The enrollment period was ultimately successful, surpassing the 7 million figure the Obama administration had predicted, but Sebelius, a former governor of Kansas, told Obama in early March she wanted to leave the administration, a White House official said.
"She believed that once open enrollment ended it would be the right time to transition the department to new leadership," an official said.
In an interview with the New York Times, which first reported on her resignation, Sebelius said she wished she could take "all the animosity" toward Obamacare with her when she departs.
"If that could just leave with me, and we could get to a new chapter, that would be terrific," she said.
Although she was most associated with the complex and politically divisive Obamacare changes, Sebelius faced a number of challenges in her time as health secretary.
When she took over in April 2009, after Senate Democrats brushed back opposition from some conservative Republicans over her support for abortion rights, she immediately had to oversee the response to a widespread outbreak of a new strain of flu that had killed scores of people in Mexico and sickened at least 64 in the United States.