Claudio Roditi was born in Rio de Janeiro on May 28, 1946, an only child in a family that moved around Brazil with his father Alberto's work in the coffee trade, including spells in Santos and in Varginha, in Minas Gerais. His father put bongos in his hands first; a cousin of his mother's gave him piano lessons from the age of six. The trumpet arrived when he was around nine, and he described the encounter as love at first sight. He learned the instrument on records by Dizzy Gillespie and Miles Davis before taking formal lessons in Rio from the saxophonist Aurino Ferreira after his father's death. In 1966 he entered the International Jazz Competition in Vienna and reached the trumpet final, where a jury that included Art Farmer told him to make a career of it. Farmer became a mentor. The earliest credit indexed under his name is Brazilian: trumpet on alto saxophonist Victor Assis Brasil's Trajeto, cut in Rio for the Equipe label in 1967, when Roditi was twenty.

He came to the United States in 1970 to study at Berklee in Boston, and stayed in the city for six years, working the local scene, hanging around the J.D.S. School of Music where he gave informal trumpet lessons, and playing again with Victor Assis Brasil, who had also landed in Boston. He met Kristen Park during those years and married her there; they were together forty-five years. In 1976 he moved to New York and started turning up on records fast: Herbie Mann's Sunbelt (Atlantic, 1978) and Mellow (1981), Dom Um Romao's Hotmosphere on Pablo, Charlie Rouse's Brazilian-inflected Cinnamon Flower (Douglas, 1977), David Schnitter's Goliath, cut at Van Gelder Studio in October 1977, a Harry Belafonte album, and two records with the Harris Simon Group alongside Michael Brecker and Joe Farrell. On several of these he is credited on valve trombone as often as on trumpet.

The turn came in 1983, when he joined Paquito D'Rivera's band. He is on Live at Keystone Korner, taped in San Francisco on June 17 and 18, 1983, credited for trumpet and valve trombone, and he stayed through four more Columbia albums to Celebration in 1988, gradually dropping the trombone. Late in 1983 the producer Creed Taylor heard him in D'Rivera's group and offered him a record of his own. Red on Red, cut at Rudy Van Gelder's studio on January 24, 25 and 26, 1984 and issued on Greene Street with a Japanese CTI edition, was both Roditi's debut as a leader and, according to its own release notes, the first Creed Taylor production and the first Van Gelder session recorded digitally. Claudio! followed for Uptown almost exactly a year later, made in a single day at Van Gelder's with Slide Hampton, Mulgrew Miller, Rufus Reid and Akira Tana. Milestone then signed him for two albums, Gemini Man (1988) and Slow Fire (recorded April 17 to 19, 1989), both produced by Helen Keane, who had spent two decades producing Bill Evans.

D'Rivera also made the introduction that put Roditi in front of the largest audiences of his career. Gillespie heard him, liked the sound, and took him into the United Nation Orchestra, the multinational big band he assembled at the end of the 1980s. Roditi is in the trumpet section on the concert at London's Royal Festival Hall on June 10, 1989, alongside Arturo Sandoval, with Slide Hampton and Steve Turre on trombones, D'Rivera and James Moody on saxophones, Danilo Perez at the piano, Airto Moreira and Giovanni Hidalgo on percussion and Flora Purim singing. Enja's recording of that night won Best Large Jazz Ensemble Performance at the 34th Grammy Awards in 1992, credited to Gillespie. Roditi returned for To Diz, With Love, taped at the Blue Note over Gillespie's seventy-fifth birthday run in January and February 1992, and he was still in the alumni band twenty years on, on the Dizzy Gillespie All-Star Big Band's Dizzy's Business (2006) and I'm BeBoppin' Too (2008).

Through the 1990s he ran two parallel careers. In New York he made a run of leader albums that alternate deliberately between Brazilian and bebop material, sometimes on the same record: Two of Swords (Candid, 1991) uses two separate quartets, one of each, and Double Standards (Reservoir, 1997) does it again six years later. Milestones (Candid, 1992) is a Birdland quintet date with D'Rivera, Kenny Barron, Ray Drummond and Ben Riley from November 1990. Free Wheelin' (Reservoir, 1994) is a programme entirely of Lee Morgan compositions, recorded on July 29, 1994 at the studio where most of the originals had been made. Alongside those he was a first-call horn for other people's projects: Horace Silver's The Hardbop Grandpop (Impulse!, 1996), Jim Hall's large-ensemble Textures (Telarc, 1997), four McCoy Tyner records, Jimmy Heath's Grammy-nominated Little Man Big Band (Verve, 1992), Slide Hampton's Dedicated to Diz, cut at the Village Vanguard in February 1993, and Tito Puente's Golden Latin Jazz All Stars at the Village Gate. In Europe he kept a completely separate band going: a trio with the German pianist Klaus Ignatzek and the Belgian bassist Jean-Louis Rassinfosse that began with Eight Languages in 1989 and produced eight more albums over the next twenty-five years, ending with For a Long Time in 2014.

The last chapter belongs to Resonance Records. Brazilliance X4, a quartet date with Helio Alves, Leonardo Cioglia and Duduka Da Fonseca recorded in March 2007 and released on February 10, 2009, was nominated for Best Latin Jazz Album at the 52nd Grammy Awards. Simpatico (2010) is entirely his own compositions, including "Altitude" for Johnny Alf and "A Dream for Kristen" for his wife, and Bons Amigos (2011) closed out the leader catalog with arrangements by Tamir Hendelman. By then he was living in South Orange, New Jersey, close enough to the local studios that several records of the period were made or mixed on his doorstep: Michael Dease's Grace was cut in South Orange on December 11, 2009, and it was in that orbit that he turned up as a guest on the Israeli guitarist Yotam Silberstein's Brasil (Jazz Legacy Productions, 2011), playing flugelhorn on one track. He taught master classes, adjudicated competitions, and spent years on the faculty of the Litchfield Jazz Camp. Prostate cancer was diagnosed in 2017 and he kept performing into 2019. He passed away at his home in South Orange on January 17, 2020, at seventy-three, survived by Kristen Park. Jimmy Heath died two days later, and the jazz press ran the two obituaries together.

Roditi is the rare player who could work both sides of the Brazilian-bebop border without treating either as a costume. He had the modern trumpet vocabulary in his hands, learned off Gillespie, Miles Davis, Clifford Brown, Lee Morgan and Booker Little records, and he had samba and bossa as first-language rhythm rather than as decoration, which is why he could program a whole album of Lee Morgan tunes one year and a direct-to-digital session in Rio the next. What separates him from the harder bop trumpeters is the attack: as Bill Kirchner observed, he tended to start solos slowly and deliberately rather than at full flame, a West Coast habit closer to Chet Baker and Gerry Mulligan than to Freddie Hubbard. The tone is the other signature. During the D'Rivera years he moved from valve trombone to the rotary-valve trumpet, an orchestral instrument with rotors instead of pistons, because in his words it gets a warmer sound than a piston horn, and he later added the piccolo trumpet; the sleeve of Mark Murphy's Night Mood is one of the few that names the rotary-valve instrument outright. Writers reaching for what the playing does with that warmth almost always land on saudade, the Brazilian word for a longing that is not quite grief. Paquito D'Rivera's summary was shorter: an original without even trying.