New York University is known for bestowing lavish perks on its leaders. Its new president, Andrew Hamilton, will be no exception.

Anticipating his January arrival from the University of Oxford, where he has been vice chancellor, N.Y.U. has been completely renovating a 4,200-square-foot penthouse duplex with four bedrooms, four and a half bathrooms and an expansive rooftop terrace. The apartment is in a landmark building at 37 Washington Square West in Greenwich Village, and it will be Dr. Hamilton’s residence, a university spokesman said.

Described by the university as “swanky” in its prior incarnation as a ceremonial presidential home, the apartment will be more opulent after the transformation, which includes moving a staircase and some existing walls and installing a new kitchen. The cost? At least $1.1 million, possibly double — raising questions as N.Y.U. and other universities are under pressure to control costs and high tuition.

The 19th and topmost floor of the building will be turned into a master-bedroom suite, where Dr. Hamilton will have private exits — one from the bedroom and one from the bathroom — onto a terrace overlooking Washington Square and, to the south, the financial district skyline, according to documents filed with New York City.