But full services at the East Side facility won't resume until February, hospital officials announced at a news conference.
Starting Monday, Bellevue also will offer limited adult and pediatric outpatient primary care clinics and routine OB-GYN services.
Limited emergency care services are expected by mid-December.
City Health and Hospitals Corp. President Alan Aviles said it's the first time in 275 years the hospital was forced to stop operations.
"It was only a few weeks ago that this historic public hospital suffered devastating damage from a monster storm that required the evacuation of all patients," Aviles said. "Our doors are once again open 24/7 while we continue the slow but certain road toward recovery with a shared sense of purpose focused, as always, on our commitment to our patients and the community we serve."
About 700 patients had to be evacuated from Bellevue when all but one of the hospital's generators failed.
Bellevue is one of four New York hospitals closed to inpatients three weeks after the storm hit the city last month. The three other medical facilities are New York University Langone Medical Center, the Manhattan VA Medical Center and Coney Island Hospital.
Patients were transported to other New York hospitals with extra beds.
Until the closure days after the storm, the National Guard aided Bellevue's efforts to stay open by hauling fuel to backup generators. But it was determined that flood damage would make it impossible to adequately power the hospital.
The fuel feed to the generators stopped working when an estimated 17 million gallons of water rushed into the hospital's 1-million-square-foot basement. The floodwaters also knocked out power to the hospital's elevators.
NYU Langone Medical Center, on the East Side near Bellevue, evacuated 300 patients after it lost generator power because of the storm. Outpatient facilities are up and running, and inpatients are expected to return in several weeks.
Coney Island Hospital also is partially reopened and due to be fully operational by January, Aviles said.
Employees from the Manhattan VA Hospital, which remains closed, have been relocated to the Brooklyn VA Medical Center.
Mayor Michael Bloomberg, working with the City Council, allocated $300 million in emergency restoration capital funds to help the city's hospitals rebuild and recover from Sandy.
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