The US General Services Administration has signed a preliminary agreement to lease 300,000 square feet at 1 World Trade Center, The Post has learned — a deal that will push the iconic tower over the psychologically crucial 50 percent-full mark.

The agency signed the term sheet — a nonbinding document that spells out all major terms and nearly always leads to a completed lease — with the tower’s owners, the Port Authority and the Durst Organization.

Although a GSA lease has been talked about for years, it never before reached the term-sheet stage until the past few days.

The deal is likely to be completed by the end of the year, sources said.

Previously, Condé Nast signed for more than 1 million square feet and China’s Beijing Vantone for 200,000 in the 3 million square-foot skyscraper.

Just as important, the GSA lease is for only half the space it originally intended to take at 1 WTC when negotiations started four years ago.

The smaller GSA commitment is a sign of health for 1 WTC, whose owners didn’t want their world-class tower filled with government agency bureaucrats.

The Port Authority and Durst are now confident of luring higher-paying private-sector tenants for the just under 1.5 million square feet that remain available.

Sources said the GSA will pay an effective starting rent on the 20-year lease in the mid-$50s per square foot, taking subsidies into account. The agency will be on floors 50-56.

Durst and a Cushman & Wakefield team led by Tara Stacom are marketing the remaining space, most of it in the tower’s highest floors.