Designed by the team of architects led by Frank Gehry, the museum was inaugurated in 1997 and is dedicated to exhibiting works of art from the Guggenheim Foundation as well as temporary exhibitions. From the beginning, the building stood out as one of the most impressive examples of deconstructivist architecture. The museum's design and construction follow Frank Gehry's signature aesthetic and methods. Similar to many of his previous works, the main structure features extremely sculpted forms that follow almost organic contours, and arguably contains no flat surfaces throughout its structure. A portion of the building is spanned by an elevated bridge, and its exterior is clad in titanium plates and a limestone that proved challenging to find (it was eventually found in Huéscar, Granada), of a shade similar to that used in the construction of the University of Deusto.

When viewed from the river, the building appears to take the shape of a ship, paying homage to the port city in which it is located. Its glossy panels resemble the scales of a fish, reminding us of the organic form influences present in many of Gehry's works. From an aerial view, however, the building takes on the shape of a flower. To conceive its design, Gehry's team made intensive use of computer simulations to determine the structures needed to support the building, achieving forms that would have been unimaginable a few decades ago.

Despite its commanding presence in views from the river level, the museum presents a more discreet appearance when viewed from the street, making it harmonize with its surroundings of more traditional buildings.