He is the youngest son of the decorator and architect Carlo Bugatti (creator and manufacturer of extraordinary furniture), the brother of Dejanice Bugatti and the car manufacturer Ettore Bugatti, and the uncle of Jean Bugatti. His first name was chosen by his godfather Giovanni Segantini, Bice Bugatti's companion. 

As a child, he began to sculpt, encouraged by the leading Lombard Divisionist painter Giovanni Segantini and by Paul Troubetzkoy, a renowned Italian and Russian sculptor and friend of the Bugatti family. Rembrandt Bugatti began modeling with plastiline. 

Rembrandt committed suicide in his studio in Montparnasse on January 8, 1916 at the age of 31 years, 2 months and 23 days. In a letter to his brother Ettore, Rembrandt Bugatti had written in 1911: "... be kind to men, kind to your wife, God to your children, and kind to animals...".

From 1944 to 1955, his remains were buried in the Père-Lachaise cemetery (97th division) before being transported to Dorlisheim.