Burwell, whose nomination must be approved by the U.S. Senate, will replace Kathleen Sebelius, who became the public face of the disastrous rollout of Obamacare, formally known as the Affordable Care Act, which Republicans plan to exploit as they seek to take control of the Senate.
The Oct. 1 launch of health insurance marketplaces was plagued by a website, HealthCare.gov, which did not work well for weeks.
Obama made it clear he did not blame Sebelius for the problems. In remarks interrupted multiple times by sustained cheering from White House and administration officials, he praised Sebelius, saying she will go down in history for her work implementing the program, meant to reduce the number of Americans without health insurance and cut into massive U.S. healthcare costs.
"She's got bumps, I've got bumps, bruises," Obama said.
"Yes, we lost the first quarter of the open enrollment period with the problems with HealthCare.gov. And there were problems," he said.
"But under Kathleen's leadership, her team at HHS turned the corner, got it fixed, got the job done, and the final score speaks for itself," he said, noting that 7.5 million people have signed up for health insurance under the program, exceeding expectations.
Burwell, 48, has served in several senior administrative roles, most recently as the head of the Office of Management and Budget.
While in the private sector, she was a member of the board of directors at MetLife.
"She gained firsthand experience into how insurance markets worked and how they could work better for businesses and families alike," Obama said.
Her appointment gives Democrats nervous about holding on to the Senate in midterm elections a chance to show the administration has turned the page on Obamacare problems.
Obama praised Burwell for her management skills and her help guiding the administration through a 16-day government shutdown last fall.
"Sylvia was a rock, a steady hand on the wheel who helped navigate the country through a very challenging time," he said.
He urged the Senate to quickly confirm her, noting her nomination as OMB director went unopposed. "I'm assuming not that much has changed since that time," he said.
Sebelius chuckled throughout Obama's speech, and spoke passionately about her accomplishments in his administration.
"This is the most meaningful work I've ever been a part of," she said.
And then Sebelius gave her critics some final fodder by declaring there was a glitch in her speech.
"Unfortunately, a page is missing," she said.