Wright's inverted-ziggurat design was not built until 1959. Numerous factors contributed to this sixteen-year delay: modifications to the design (all told, the architect produced six separate sets of plans and 749 drawings), the acquisition of additional property, and the rising costs of building materials following World War II. The death of the museum's benefactor, Solomon R. Guggenheim, in 1949 further delayed the project. It was not until 1956 that construction of the museum, renamed in Guggenheim's memory, finally began.

Frank Lloyd Wright's masterpiece opened to the public on October 21, 1959, six months after his own death, and was immediately recognized as an architectural landmark. The Solomon R. Guggenheim Museum is arguably the most important building of Wright's late career. A monument to modernism, the unique architecture of the space, with its spiral ramp riding to a domed skylight, continues to thrill visitors and provide a unique forum for the presentation of contemporary art. In the words of Paul Goldberger, "Wright's building made it socially and culturally acceptable for an architect to design a highly expressive, intensely personal museum. In this sense almost every museum of our time is a child of the Guggenheim."

Solomon R. Guggenheim Museum Annex, 1985–92

Frank Lloyd Wright's original plans for the Solomon R. Guggenheim Museum called for a ten-story tower behind the smaller rotunda, to house galleries, offices, workrooms, storage, and private studio apartments. Largely for financial reasons, Wright's proposed tower went unrealized. Gwathmey Siegel & Associates Architects revived the tower plan with its eight-story annex, which incorporates the foundation and framing of a smaller 1968 annex designed by Frank Lloyd Wright's son-in-law, William Wesley Peters.

In 1990, the Wright building was closed to the public to enable the expansion and a major interior restoration, which was overseen by the firm. The restoration opened the entire Wright building to the public for the first time, converting spaces that had been used for storage and offices into galleries. The restored and expanded Solomon R. Guggenheim Museum reopened in 1992, and the project became one of the firm's most celebrated and critically acclaimed works. It contains 4,750 square meters of new and renovated gallery space, 130 square meters of new office space, a restored restaurant, and retrofitted support and storage spaces.

Gwathmey Siegel & Associates' subtle intervention greatly improved the exhibition capabilities of the museum without detracting from Wright's original design. The tower's simple facade and grid pattern highlight Wright's unique spiral design and serves as a backdrop to the rising urban landscape behind the museum.