He began to study the viola in the early 1950s and switched to this instrument on a full-time basis when was invited by Pina Carmirelli and Arturo Bonucci to replace Renzo Sabatini in the Quintetto Boccherini.
Bonucci and Carmirelli had just bought in Paris a complete collection of the 141 string quintets by Luigi Boccherini, and set about to promote this long forgotten music.
After the deaths of Bonucci and Carmirelli, Luigi Sagrati became the main force behind the success of the Quintetto Boccherini, which ceased its activities in the 1990s, when he had to stop performing professionally because of his age.
Sagrati also founded the Brahms Quartet for strings and piano with Piero Masi (pianoforte), Marco Scano (Cello) and Montserrat Cervera (violin).
From 1977 to his death he was president of the Unione Musicisti di Roma, with whose chamber orchestra he worked to spread musical culture in the Latium region.