Shake Shack is finally coming to the Village — the East Village, as it happens.

Danny Meyer’s fast-growing burger chain has signed a lease on Astor Place that will open this fall, The Post has learned.

The new location, which will span nearly 3,000 square feet on the northeast side of the building at 51 Astor Pl., “will feature some unique design and customer experience elements,” a Shake Shack spokeswoman confirmed, declining to elaborate.

The retail spot also has 18 feet of frontage on the open plaza on the ground floor of the dark-glass office building, which until recently had no retail space available.

But in March, with just one $4.05 million apartment left to sell and the Public Hotel opening next month, Ian Schrager folded up his sales office at 51 Astor for his condominiums at 215 Chrystie St. leaving the spot facing Ninth Street and Third Avenue vacant.

The 15-year lease for the burger joint has one, five-year option and was quietly signed in March.

The lease memo, reviewed by the Post, provides the Danny Meyer fast-casual joint with the ability to exclusively sell “hamburgers, hot dogs, French fries and frozen custard.”

As such, it banishes direct competitors such as Smashburger and Johnny Rockets from the building. Non-burger-slinging tenants already in the building include Chop’t, Bluestone Lane and Flywheel Sports.

Among 51 Astor’s office tenants is IBM Watson. The project was developed and is owned by Edward J. Minskoff Equities on land leased from Cooper Union.

A CBRE team of Andrew S. Goldberg, Matt Chmielecki and Preston Cannon repped the eatery.

Patrick Smith, Matt Ogle and Corey Zolchinski of JLL repped the ownership in the deal.