The newspaper said the sale of the building, situated just a stone's throw from the White House, to a property firm would be sealed by March next year for $159 million.
The paper, which is now owned by Amazon founder Jeff Bezos, will continue to rent space in the building until a new headquarters is found.
The Post's search for new premises had begun before Bezos bought the paper earlier this year.
The Post's current headquarters was the paper's base during its most famous hour, when journalists Carl Bernstein and Bob Woodward uncovered the Watergate scandal that ultimately led to the resignation of Richard Nixon as President.