He is the first such service member to receive a double arm transplant, and the hospital says he is one of only seven people in the United States who have undergone successful double arm transplants.
The hospital said it would detail the operation at a news briefing Tuesday. The operation was performed Dec. 18.
Later, in a new antirejection procedure, he received an infusion of bone marrow derived from vertebrae harvested from the donor's lower spine. The infusion lets doctors reduce the number of powerful antirejection drugs from three to one.
Antirejection drugs can have harmful side effects, such as infection, organ damage, and cancer.
The surgery was done by a team of transplant experts headed by W.P. Andrew Lee, chairman of the department of plastic and reconstructive surgery at the hospital. It was the first limb transplant by his newly established group at Hopkins, the hospital says.
"He's doing well," Marrocco's father, Alex, said Monday. "It's been a little over a month now."
Lee, in an interview, said there have been about 80 arms transplanted in about 60 patients around the world.
There are hundreds of military amputees around the country, including four others who have lost four limbs.
Most quadruple amputees have been fitted with - and mastered - sophisticated mechanical prostheses. But research has suggested that younger amputees do not always use them, Lee said in a recent interview.
"The nonacceptance rate of prosthetics is highest among young people in their 20s and 30s," he said.
So the possibility of limb transplantation, despite its medical, psychological and logistical complexity, holds great promise, he said.
Results have been good, Lee said, although the arms are never going to return to 100 percent of their former function. Patients have learned to tie shoes, use chopsticks, and put their hair in a ponytail, he said.
"I think it also has additional advantage for the patient to be restored whole," he said. "Once they're transplanted, they regard the arm as theirs. And . . . they're more comfortable going out on social occasions, as opposed to wearing a prosthetic."
Marrocco, a fair-skinned young man with a shock of light-colored hair, has not spoken widely of the operation.
After recovering at the old Walter Reed Army Medical Center in Washington, he returned to Staten Island, where a special home was reportedly constructed for him by charitable groups.
He has endured numerous surgeries and return trips to the hospital, and had been anticipating a transplant since 2010.