The city invited the public Monday into the new $200 million wing of Gouverneur Healthcare Services, which initially served 19th-century immigrants on the Lower East Side and now treats the 21st-century immigrants of Chinatown.

The center — now with 13 stories of newly built glass and steel wrapped around a red-brick hospital — is overhauling and expanding its nursing home and ambulatory care center.

The building project includes a five-story addition to the historic complex, topped by an eight-story tower that will serve as the nursing home. Each floor of the nursing home features a central fireplace and gathering area, and residents will no longer have to share rooms.

Director Mendel Hagler said nearby nursing homes have closed, and local clinics haven’t kept pace with the growing population.

“There’s not enough primary care doctors," Hagler said. "There are not enough spaces for patients to go to. There are not enough clinics. There are not enough private doctors — and particularly in Lower Manhattan, where we’re so densely populated.”

Mendel said the overhaul will help integrate primary and specialty care for tens of thousands more patients a year.

“We’ve done everything with the thought process: how do we make it more efficient for the patients, and how do we make it more efficient for the doctors? And I think the savings is really there,” Mendel said.

Gouverneur’s ambulatory care center will serve about 400,000 patient visits. Its expanded nursing home will house about 300 residents, instead of 200. Most will be short-term residents, recovering from medical treatment, and about a third will be long-term nursing home residents.