Carmona and Dr. Elias Zerhouni, executive vice dean at Johns Hopkins School of Medicine, must be confirmed by the Senate before filling the two top health policy and research positions.
The president was announcing their nominations, which were confirmed by a senior administration official and a congressional source, at a ceremony Tuesday afternoon in the White House.
At NIH, the nation's premier biomedical research agency, the top post has been vacant for more than two years.
Mr. Bush has been looking for a surgeon general ever since David Satcher, President Clinton's appointment, announced last year that he would step down when his four-year term ended last month.
Carmona evidently dazzled Bush's selection team with a resume that reads like a Hollywood script. "He's somebody who's risked his life to save lives. He's dangled out of helicopters to save people," said the administration official in advance of the president's announcement.
Carmona, 52 and registered as an independent, was born in Harlem. He dropped out of high school, joined the Army and earned a G.E.D. He then became the first member of his family to graduate from college and medical school.
In 1992, the doctor grabbed headlines and inspired a made-for-TV-movie by rappelling from a helicopter to rescue a person stranded on a cliff. This and other feats helped him earn one of 10 Top Cop awards from the National Association of Police Organizations in 2000.
In 1999, Carmona happened upon a car accident in Tucson, and stopped to help. Instead, he got into a shootout with one of the drivers.
The man, who had been assaulting a female driver, died, but not before Carmona attempted to mend his fatal wounds. The man turned out to be a suspect in the murder of his own father.
Carmona's scalp was grazed by a bullet, his second wound in the same place. He got the first while fighting in Vietnam as an Army Green Beret.
In 1985, he created the first trauma care system in southern Arizona. A year later, he joined the Pima County Sheriff's Department as a SWAT team member.
For the NIH position, Zerhouni, 50, met the administration's twin goals of finding a respected scientist who could live within Bush's ethical constraints on controversial research involving cloning and embryonic stem cells.
His background is in radiology, and he has chaired the university's radiology department.
Surgeon general and NIH director are two of several important federal health jobs that have gone vacant while Bush advisers searched for replacements for Clinton appointees.
The NIH has struggled in the two years without a director since the departure of Harold Varmus, with several top researchers leaving. Six institutes of the NIH institutes need new directors, positions that are expected to be filled now that the top job has been settled.
The top position at the Food and Drug Administration has been empty for a year.
The National Institutes of Health pay for more than 2,000 biomedical projects in the United States and employ more than 10,000 people. Its budget has been steadily rising over the last several years, with Bush asking for more than $27 billion for next year.
As Surgeon General, Carmona would, among other things, administer the 56-member Public Health Commission, which was deployed to New York and Washington on Sept. 11 and during the subsequent anthrax attacks.