The city has given Fashion Week its cat-walking papers from Lincoln Center.

The de Blasio administration folded like a cheap suit — settling a lawsuit filed by parks advocates that demanded the star-studded extravaganza leave the Upper West Side venue because it encroaches on a small park nearby.

“IMG Fashion Week shall vacate the premises and remove all tents and other Fashion Week equipment from the park,” according to the settlement, signed by New York Supreme Court Justice Margaret Chan on Tuesday.

Fashion Week — which generates an estimated $865 million for the city annually — was supposed to stay at Lincoln Center until 2020, when it would have a permanent home at Hudson Yards.

Now, its last show at Lincoln Center will be in February.

Organizers are eyeing event spaces downtown — which fashionistas say could strip away the glitz.

“You can’t top those gorgeous street-style photos of well-heeled women in front of the fountain in Lincoln Center,” said Harper’s Bazaar editor Joyann King.

She added, “It’s such a landmark of the city . . . Lincoln Center had an elegance about it. There will be a little bit of that lost.”

Meghan Manning, a 22-year-old dancer who performs at Lincoln Center added, “I liked having it here. It’s iconic.”

NYC Parks Advocates and other green-space boosters sued the city Parks Department in 2013 for misusing Damrosch Park, which is adjacent to Lincoln Center.

The settlement requires the city to add more trees and to hang a sign proclaiming that the space is a public park.

“Damrosch Park belongs to the city of New York not Lincoln Center,” Geoffrey Croft of NYC Park Advocates posted on his blog, A Walk in The Park.

Some neighbors also cheered the terms of the settlement.

“We are thrilled at the current settlement and that the park will be rebuilt,” said Cleo Dana, the chair of Friends of Damrosch Park, a plaintiff in the lawsuit.

A Fashion Week spokesman said the venue was good while it lasted.

“Lincoln Center has been a great home . . . However, as the fashion industry continues to evolve, IMG has been actively looking for a new home hat gives our designers and partners the best possible environment to share their creative visions,” a Fashion Week spokesman said.

Additional reporting by Amber Sutherland