Armando Trovajoli (the family name is also spelled Trovaioli, and many of his records use that form) was born in Rome on September 2, 1917. He began on the violin as a child, then took a diploma in piano and composition at the Santa Cecilia conservatory in Rome. His jazz apprenticeship came before the diploma, which he completed in 1948. In 1937 he joined the orchestra of Rocco Grasso, who made him the band's pianist the following year, and in 1939 he played with the orchestra of Sesto Carlini, one of the best-regarded Italian jazz ensembles of the period. From 1940 to 1943 he served as an army officer, sent to the Balkan front and later posted near Rome, and he was discharged in 1944.

When the Allies reached Rome that year he formed Il club del ritmo with guitarist Libero Tosoni, and the group played the city's clubs and theatres. After the war he kept alternating jazz with light music. In 1949 he was chosen to represent Italy at the international jazz festival in Paris, where he played the Salle Pleyel with Gorni Kramer on bass and Gil Cuppini on drums. The festival bill also carried Charlie Parker and Miles Davis.

The first run of recordings dates from 1950 and 1951, issued on Parlophon under the series title Musica per i vostri sogni. They include trio 78s with Franco Cerri and drummer Paolo Tagliaferri (Body and Soul and Lullaby in Rhythm, What Is This Thing Called Love), solo-piano sides on Fascinating Rhythm and Sophisticated Lady (November 1950), and, in 1951, Yesterdays, Easy to Love, Lady Bird and All the Things You Are, one side of them with a string orchestra. One 1950 disc pairs his trio on Big City Blues with a side by the Roman New Orleans Jazz Band. In the same years RAI gave him a light-music orchestra built around strings, harp, vibraphone, electric guitar and his own piano, and Italian Wikipedia describes its radio broadcasts as having a clear jazz orientation. In 1952 and 1953 he and Piero Piccioni alternated as conductor of the weekly broadcast Eclipse, an unusually refined program for radio orchestras of the time. He also appeared as a soloist in Gershwin repertoire in 1951, at the Teatro San Carlo in Naples and at the Basilica of Maxentius in Rome.

Film work then became the larger part of his life. He shared the score of Bitter Rice (1949) with Goffredo Petrassi, and in 1951 he wrote music for Anna, including the song El Negro Zumbón, an international hit. By the end of his career he had composed or conducted more than 300 scores, working with Vittorio De Sica, Dino Risi and, across almost his whole filmography, Ettore Scola; English Wikipedia notes that many of the scores for Commedia all'italiana comedies were jazz scores. He conducted the Sanremo Festival orchestra in 1953 and arranged the winning song, Viale d'autunno, and he wrote the Garinei and Giovannini musicals Rugantino (1962), Ciao Rudy and Aggiungi un posto a tavola, with Roma nun fa' la stupida stasera from Rugantino becoming his best-known song. He married the actress Pier Angeli in 1962 (they divorced in 1969) and received the David di Donatello career award in 2007.

The most concentrated jazz documentation falls between 1958 and 1963. RAI's light-music orchestra in Rome, which he founded in 1958 and which Kramer, Lelio Luttazzi and Piero Piccioni later directed, was one outlet; the saxophonist Gianni Basso worked in a radio orchestra under Trovajoli from 1956 to 1958. On RCA Italiana he recorded the orchestral album Songs by Night (1958), then two piano-trio albums with Berto Pisano on bass, Sergio Conti on drums and Enzo Grillini on guitar: Trovajoli Jazz Piano (1959), with Round Midnight, Walkin' and Have You Met Miss Jones, and Softly (1959), which adds Gino Marinacci on flute. A February 1960 seven inch, Round Midnight, carries three of those trio performances. His quartet's Round Midnight was one of the Italian jazz selections on RCA's 1960 compilation Il Jazz in Italia: 4 Dimensioni, next to the Romano Mussolini Quartet and the Nunzio Rotondo Quartet. The Beat Generation (1960) is the big-band record: a big band credited with six trombones, five trumpets and seven saxophones, including Basso, Oscar Valdambrini, Dino Piana, Gino Marinacci, Livio Cerveglieri, Attilio Donadio and Baldo Panfili, playing arrangements by Trovajoli on pieces such as Blues and Bonjour Tristano. In 1963 he followed with a three-volume Gershwin series for RCA Italiana, with Nora Orlandi's vocal group.

He remained a public presence in Rome into his nineties. In Casa del Jazz's 2008 tribute recording Omaggio a Armando Trovajoli, made on March 20, 2008 by the Dino e Franco Piana Jazz Orchestra with arrangements by Franco Piana, he plays piano himself on two tracks, Piaceva alle donne and Roma nun fa' la stupida stasera, while Enrico Pieranunzi takes the piano on a third. He passed away in Rome on February 28, 2013, at 95. The Museo di Roma in Trastevere marked the tenth anniversary with the exhibition Armando Trovajoli. Una leggenda in musica, which ran from March 11 to May 14, 2023.

Trovajoli's jazz is a pianist's and an orchestrator's jazz that sits close to the light-music world he also worked in. The 1950s trio records favor standards (Porter, Kern, Rodgers and Hart, Monk's Round Midnight) played in a clean, swinging, melodic style with bass, drums and guitar behind him, and the later RCA catalogue is filed under jazz with swing, cool jazz and easy listening as style tags. The Gershwin records of 1963 and a 1970 promotional LP on the same repertoire show where his affections lay: American songbook material treated by a large orchestra with a vocal chorus. The Beat Generation points in a more modern direction, with a title track and a piece called Bonjour Tristano whose title nods to the pianist Lennie Tristano.

He should be read plainly as a film and theatre composer who was also a working jazz pianist, not as a jazz specialist. His own phrasing and orchestration move between jazz, popular song and screen music with little friction, which suits the jazz-flavored comedy scores English Wikipedia singles out. A 2023 exhibition text describes him as a jazz lover who played with many leading jazz musicians and names Duke Ellington, Miles Davis, Chet Baker, Stéphane Grappelli and Django Reinhardt, but the dates and settings of those meetings are not documented in the sources consulted, so they are not treated here as recorded collaborations.