The Metropolitan Transit Authority has approved a $1 billion deal to convert a stretch of land along New York City’s Hudson waterfront into a sprawling development.

Under the agreement Wednesday, developer Related Companies will be required to pay $20 million when the contract is signed and another $21.7 million in the next 12 months.

It allows Related to delay closing until office vacancy rates drop to 11 percent and co-op and condo prices hit $1,200 per square feet.

The MTA owns the land known as Hudson Yards for Long Island Rail Road operations.

In December, the City Council approved a rezoning plan for half of the 26-acres for apartments, cultural space and a new public school. The other half was rezoned in 2005 and allows for office, hotel and retail space and public open areas.