Top designer Michael Kors is purchasing a posh penthouse at The Greenwich Lane — a 200-unit development in five buildings and five townhouses that stands on what was once the site of St. Vincent’s Hospital.

The penthouse is a three-bedroom, 31/2-bathroom unit that is in the “$17 million to $21 million range,” a source said.

It includes an eat-in chef’s kitchen and a private rooftop terrace with views of the Empire State Building.

The Greenwich Lane, which is LEED certified, features interior design by Thomas O’Brien.

While the building is 70 percent sold, the Rudin family and Global Holdings, which are developing the complex, are not commenting on buyers, a spokesperson said. Kors did not return calls.