Diego Urcola was born in Buenos Aires on November 5, 1965, into a household where music was the family trade. His father Ruben directed the music department at Colegio Ward, and Urcola began formal study there at nine, starting on trumpet in a school band good enough to give him work no other Buenos Aires school could. Because he was one of the few players who could switch instruments, he spent his boyhood covering euphonium, French horn, tuba and percussion parts as the band needed them, a habit of doubling that never left him. He went on to the Conservatorio Nacional de Musica, where the curriculum was entirely classical, and took the title of profesor nacional de música in 1988. Jazz he had to find on his own: a handful of CTI-era records that reached Argentina, his father's Prestige albums, a Dizzy Gillespie and Oscar Peterson duet record. Jazz gigs in the city were early-week affairs played mostly for love, so he made his living on theatre pit work, television and studio calls, and rock sessions, among them the trumpet on Soda Stereo's Signos and Juan Carlos Baglietto's Acné, both cut in 1986.

A scholarship took him to Boston in 1988, and the Berklee College of Music turned out to be less about classes than about rooms. "I was playing two or three jam sessions or rehearsals every day," he told R.J. DeLuke in 2011. "That was when I really learned." His year group there included Danilo Pérez, Mark Turner, Chris Cheek, Antonio Hart, Roy Hargrove, Kurt Rosenwinkel and Geoffrey Keezer. A Tower Records opened a few blocks from the school and he spent his money there on the Blue Note catalogue he had never been able to hear. He took his diploma in jazz performance in 1990, stayed in Boston a further year working Latin gigs, and made his first American record in that period: one track of Orange Then Blue's Funkallero, taped at the Majestic Theatre in Boston on November 15, 1989.

He moved to New York in 1991 and the break came almost at once. Claudio Roditi left Paquito D'Rivera's quintet, friends put Urcola's name forward, and he has held the trumpet chair ever since, a run of more than three decades that he describes plainly as the reason he is still working. The first years were spent largely on the road with that band, and the D'Rivera connection opened most of the others: touring in the mid-1990s with Slide Hampton in a group the trombonist called The Jazz Masters, and with the United Nation Orchestra, the band Dizzy Gillespie founded and D'Rivera led after his death. He worked briefly with Wynton Marsalis, including a Lincoln Center Jazz Orchestra appearance at the 1996 Olympic Games in Atlanta. He kept studying while he worked, taking a master's in jazz performance from Queens College in 1997, at a school whose jazz department Jimmy Heath anchored, and that same year he placed second in the Thelonious Monk International Jazz Trumpet Competition.

The late 1990s brought calls from a generation above his own. Joe Henderson took him into his band; the trombonist Steve Turre used him in Sanctified Shells; he played with the Carnegie Hall Jazz Band and with Wayne Shorter on the ABC television special The 2nd Annual Celebration of America's Music, and in 1999 Milt Jackson called him into an all-star big band. He was also becoming a fixture of the downtown scene his own generation was building, playing in Jason Lindner's Monday big band at Smalls and turning up on the Impulse! anthology Jazz Underground: Live at Smalls. He also played trumpet on Wind from the South, the Verve debut of the Chilean singer Claudia Acuña, and in that same year, 2000, he joined the International Vamp Band that the bassist Avishai Cohen had founded, one thread of a working relationship that already stretched back to 1995 and would run for nearly twenty years. The same period tied him to his fellow Argentine Guillermo Klein, whose band Los Guachos has carried Urcola's horn on five records from 1999 to 2016.

His own catalogue began in the middle of all this. Libertango was recorded in a single day at Seltzer Sound in New York on March 8, 1995, with Chris Cheek, Edward Simon, Avishai Cohen, Adam Cruz and the bandoneonist Raul Jaurena, produced by Klein, and released on Fresh Sound World Jazz in 1999. Soundances (Sunnyside, 2003) he cut in Buenos Aires with two separate local rhythm sections, and it drew nominations at both the 2004 Latin Grammys and the 2005 Grammy Awards for Best Latin Jazz Album. Viva, recorded at Bennett Studios in New Jersey over three days in November 2005 and issued by CAM Jazz in 2006, is the most heavily staffed of his records: a core quintet of Edward Simon, Avishai Cohen, Antonio Sanchez and Pernell Saturnino with guest turns from D'Rivera, Dave Samuels, Jimmy Heath and the trombonist Conrad Herwig, and it brought a second Grammy nomination in 2007.

D'Rivera is also the reason Urcola plays valve trombone. Roditi had used one in the early New York quintets and D'Rivera liked how it blended; when Urcola declined to take it up, D'Rivera turned up at his apartment with a new Yamaha and told him to bring it to the Blue Note. He first recorded on it for Funk Tango, the 2007 debut release of D'Rivera's own label and the winner of the 2008 Grammy for Best Latin Jazz Album, and it has been a standing double ever since, in D'Rivera's quintet, in Los Guachos, in the Caribbean Jazz Project he joined in 2004, and on his own dates. Three further D'Rivera records he plays on took the Latin Grammy for Best Latin Jazz Album: the quintet's Live at the Blue Note in 2001, Panamericana Suite in 2011 and Jazz Meets the Classics in 2015.

The later leader records narrow rather than widen. Appreciation (CAM Jazz, 2011) is a piano quartet with Luis Perdomo, Hans Glawischnig and Eric McPherson, and its nine originals are each dedicated to a musician who shaped him: Freddie Hubbard, Hermeto Pascoal, D'Rivera, Mario Rivera, Klein, Astor Piazzolla alongside Miles Davis, Wayne Shorter, Woody Shaw with Dizzy Gillespie, and John Coltrane. Mates (Sunnyside, 2013) goes further still, fourteen pieces played entirely in duo with four partners recorded separately in four studios: Avishai Cohen on bass, Dave Samuels on vibraphone and marimba, Edmar Castaneda on harp and Juan Dargenton on bandoneon. El Duelo (Sunnyside, 2020) sets a piano-less quartet with the bassist Hamish Smith and drummer Eric Doob against D'Rivera on alto saxophone and clarinet, working through Ornette Coleman, Gerry Mulligan, Kenny Wheeler, Thelonious Monk, Benny Golson, Osvaldo Pugliese and Piazzolla alongside his own tunes.

He has remained one of the busier trumpet chairs in New York's Latin and straight-ahead circles: five trumpets deep in the Jimmy Heath Big Band on Togetherness, recorded at the Blue Note in October 2011 beside Roy Hargrove, Frank Greene, Greg Gisbert and Michael Philip Mossman; in Enrico Pieranunzi's Latin Jazz Quintet at Birdland and his later quintet at the Village Vanguard; on Brian Lynch's Woody Shaw project Madera Latino; and on Miguel Zenón's Golden City, recorded in November 2023. He teaches as well, giving master classes and clinics, among them a Latin and Latin jazz trumpet-styles session at his old school Berklee in March 2019.

Urcola is a Latin jazz musician in the sense that matters least to him and a bebop-descended improviser in the sense that matters most. "I like to bring the tango flavor from my country into the mix," he has said, "but, foremost I'm a jazz musician," and elsewhere he has been blunter about what he thinks he is doing: "It's not about swing or Latin or whatever type of rhythm or elements. It's a concept of improvisation and interaction." His trumpet playing is bright, fast and clean-edged, built on the CTI-era Freddie Hubbard records that were the only ones available to him as a teenager in Buenos Aires and on the Miles Davis albums in his father's collection, and audibly indebted to Dizzy Gillespie, whose bands he never played in but whose sidemen, D'Rivera, Slide Hampton and Jimmy Heath, employed him for decades. Wayne Shorter is the influence he names on his writing: harmonies, structures, and the way a melody is developed. What distinguishes him from the many capable Latin jazz trumpeters of his generation is the doubling. He plays flugelhorn and, since around 2006, valve trombone with enough command that leaders write for it, and he uses the trombone's tenor register as a second voice rather than a colour, so his own quartet records can move from soprano to tenor range without adding a player. His compositions do the same thing structurally, setting an Afro-Peruvian landó or a milonga under a post-bop line rather than laying a jazz solo over a Latin groove, which is why AllMusic's Matt Collar describes him as a player who "infuses post-bop jazz with South American traditions" rather than the reverse.