As the steel industry boomed in Pittsburgh during the last quarter of the nineteenth century, the population of the city grew. New residents required federal services, so Pittsburgh native and Secretary of the Treasury Andrew W. Mellon helped to allocate funds for a new federal building in his hometown. Mellon supported the construction of a building that would represent the rise of Pittsburgh and western Pennsylvania to national political and economic prominence.
The New York architectural firm of Trowbridge & Livingston designed the building under the auspices of Supervising Architect of the Treasury James A. Wetmore. Construction commenced in 1931 but stopped shortly thereafter due to a labor dispute. The strike ended and construction resumed on June 8, 1932. The building was erected over the rail line in order to eliminate transporting mail to and from stations. It was completed and opened to the public on October 13, 1934 amid much fanfare, as was typical for federal building dedications during the Depression era, when federal buildings were symbols of hope for economic recovery and social stability. The Western District of Pennsylvania gaveled in its first court session in the building on November 7, 1934. Referred to as the New Federal Building until 1964, when another federal building was built across the street, it was the city's main postal distribution center until the majority of postal functions moved to a new facility in 1983. General Services Administration (GSA) acquired the building the following year.
During the 20th century, the building underwent several significant interior alterations, which included the addition of new courtrooms and the removal of the train tracks. Renovations that began in 2002 involved the modernization of existing courtrooms and the installation of six new courtrooms and judge's chambers to accommodate the growing needs of the courts. Lobby spaces were restored, and the building's exterior was cleaned and re-pointed.
The U.S. Post Office and Courthouse is a contributing building in the Pittsburgh Central Downtown Historic District, which was listed in the National Register of Historic Places in 1985. Ten years later, the building was individually listed in the National Register of Historic Places as the US Post Office and Courthouse-Pittsburgh. The renovation design received a citation at the 2001 GSA Design Awards Ceremony. In 2015, the building was renamed for Joseph F. Weis Jr., a judge in the Third Circuit Court of Appeals.
The Grant Street Station Post Office, which had been in the Seventh Avenue section of the building since its opening, closed permanently at 2:00 p.m. EST on Saturday Afternoon, February 15, 2014. Glenn A. Walsh, who had leased a post office box in this Post Office for more than 25 years, was the last member of the general public in the Post Office at the time of closing.