Built for Secretary of the Treasury Franklin MacVeagh, whose Chicago residence had been designed by H. H. Richardson, 2829 16th Street served as the Mexican Embassy beginning in 1921, at which time the overscaled Tuscan porte-cochere was added to a somewhat stark urban villa notable on Meridian Hill for its relative plainness. Wyeth's design was unusual among its contemporaneous neighbors in the simplicity of its self-contained form and the predominance of buff-colored brick, which set it apart from the elaborately sculpted and more colorful mansions common to the area. The building is a vertically oriented rectangle of four stories (the top two of which read as attic stories with minimal fenestration). The relatively small amount of window area in comparison to plain, unbroken wall surfaces emphasizes the sense of tautly contained volumes within.

The Mexican Embassy relocated its offices to 1911 Pennsylvania Avenue in 1989, at which point the Mexican Cultural Institute established its presence at the mansion.