Born in Rome, Brindisi was trained by his father, a skilled wood carver, in Pescara and L'Aquila.
He came into contact with Ardengo Soffici and Ottone Rosai in Florence in 1940 and held his first solo show there, with a presentation by Eugenio Montale.
As a result of a move to Milan, the post-war period saw a short phase marked by the influence of Cubist painting as interpreted in an expressionistic and existential sense.
Brindisi formed the Gruppo di Linea together with Gianni Dova and Ibrahim Kodra and was later associated with the realist movement, while maintaining, however, complete autonomy with respect to the major artistic trends of the age.
The 1970s and ’80s saw the continuation of the same repertoire distinguished by intense and violent colour and characteristically flattened figures in two-dimensional space.