The house that was previously present on the plot of the current Hotel Cueto, was bought by Ramón López Fernández in 1905. Ramón had an intention to build a new building with the ground floor being used for the storage of merchandise. The little-known architect Arturo Marqués undertook the construction of the building that began in 1906 and was completed in 1908. Initially it was used as a warehouse and then as the hat shop of Ramón López y Compañía until 1920s. In 1910 the Spanish merchant José Cueto y Suárez rented the building. When he bought it in 1927, he converted the building into a hotel, Hotel Palacio Viena. The building had a beautiful pharmacy on the ground floor, with a splendid cedar counter and outstanding wood carving. Later, it became an apartment building. Gradually it deteriorated and became a tenement house with a warehouse on the ground floor towards 1990s. Since then, it was left empty and unused until 2005 when restoration works began in the building. Finally in 2019, it reopened its doors, now converted into an extraordinary luxury hotel with 60 rooms and all the services that a facility of its type demands. Currently it is managed by the company Hoteles Habaguanex of the Gaviota Tourism Group.

The building has a façade adorned with griffin, satyr and other figures from Greek mythology. The griffin is a legendary creature with the body, tail and back legs of a lion, the head and wings of an eagle, and the front feet the talons of an eagle. As both the animals are considered the kings of their category, the powerful griffin was thought of as king of all creatures. A satyr is the member of a troop of ithyphallic (having the penis erect) male companions of Dionysus (God of the grape harvest, winemaking and wine, of ritual madness, fertility, theatre and religious ecstasy in ancient Greek religion and myth). They usually had horse-like ears and tails, as well as permanent, exaggerated erections. The ornate façade has an appearance reminiscent of the modernist constructions built by some Catalan architects in Barcelona (such as Lluís Domènech i Montaner and Josep Puig i Cadafalch), but particularly by the genius Antonio Gaudí y Cornet (1852-1926). Arturo Marqués might have been inspired by the new European trends in the early years of the 20th century in constructing this unique modern building that is the first and perhaps the most famous art nouveau building in Havana.

From the mid-19th century on, a desire for the modernity emerged in Cuba, so that the first modern constructions began in 1883. In 1900s art nouveau was espoused by the Cuban architects as a rejection of the colonial style. Even though some magazines propagated the ideas of modernity, the art nouveau did not become widespread in Cuba. It was the art deco that took root in Havana for its simplicity in comparison to art nouveau. The Habana Vieja is the place that shelters the largest number of art nouveau buildings in the capital.

The colossal male figures are used as columns, as well as the female caryatids that protrude above the arcade of the main entrance. The Greek term caryatid is a sculpted female figure serving as an architectural support taking the place of a column or a pillar supporting an entablature on her head. The true architectural jewel is a magnificent stone work with balconies in the shape of waves. This feature reminds Gaudí’s works in that he always tried to add the nature to his works.

The rich-ornate façade of the Hotel Palacio Cueto that distinguishes it from all of the other surrounding buildings, was featured in the Cuban movie Vals Para La Habana in 1988.