The palace was probably built in the early Seventeenth century by a branch of the Medici where the ancient Soderini Palace once stood. From 1805 the owner Antonio Schneiderff kept it as an inn, and it become a much loved place for foreign travellers: scholars, historians and intellectuals such as Walter Scott, George Byron, Stendhal, and John Ruskin were guests there.

In 1850 Pastor Robert Hanna of the Free Church of Scotland arrived and the congregation was housed in Palazzo Baldovinetti by the Reformed Church. A separate chapel was later established at number 19.

The palace is now home to the Maison Coveri and its art gallery.