The palace was built in the first half of 16th century by Filippo Adimari, Camerlengo of Pope Leo X, on a plot of land for vineyard owned by Orazio Farnese.

In 1794 the palace passed to the House of Borghese and, after other transfers of property (Paccanari, Lavaggi), in 1840 it was bought by the Papal State and used as the seat of the city archive and of a botanical garden.

During World War II, in the period of the Nazi occupation, the rooms of the military college were used to lock in for some days (from 16 to 17 October 1943) a thousand Jews captured during the roundput in the Roman ghetto, before they were deported.

The palace now houses the Istituto Alti Studi per la Difesa, with an important library specialized in military and geopolitical disciplines.

In front of Palazzo Salviati formerly rose the Trastevere headboard of the Ponte dei Fiorentini, an iron suspension bridge built in 1863 close to the church of San Giovanni dei Fiorentini as an additional connection between the historic centre and the new quarter of Prati, then under construction.