Josh Evans grew up in Hartford, Connecticut, and took up the trumpet at age 10 after hearing a recording of Roy Eldridge and Dizzy Gillespie. He began lessons with Raymond "Dr. Rackle" Williams and within a year was performing regularly in Williams's Sound Griot Brass Band. At 14 he started studying with alto saxophonist and composer Jackie McLean, a mentorship that shaped both his playing and his musical outlook for years afterward; through McLean, and through performances alongside him at the Blue Note, Iridium, the Regattabar in Boston, and the Bushnell Center for Performing Arts in his hometown, Evans got an early, direct education in the hard-bop tradition.

In April 2005 Evans joined drummer Winard Harper's sextet, touring the United States for roughly three and a half years and recording Make It Happen (2006, Piadrum Records) alongside altoist Antonio Hart, trombonist Wycliffe Gordon, tenor saxophonist Stacy Dillard, and fellow young trumpeter-turned-labelmate Lawrence Clark, who plays tenor saxophone and would go on to become one of Evans's closest recurring collaborators. In April 2007, Evans was invited on a two-week tour of Siberia with saxophonist Benny Golson. Around the same time he began performing with drummer Rashied Ali, stepping into the trumpet chair of Ali's working quintet that trumpeter Jumaane Smith had held on the band's Judgment Day, Vol. 1 and Vol. 2 (recorded February 2005). Evans has named Ali, alongside McLean, as one of the two biggest influences on his playing, and has said Ali introduced him to Marion Brown's Bout Soul, an album that left a lasting mark on his musicianship. He remained the group's trumpeter for roughly the last two to three years of Ali's life, touring an estimated 18 to 20 countries with the band. The only commercial recording of that lineup with Evans aboard is Live In Europe (Survival Records SR 126), taped November 2, 2007, at the Jazz Happening festival in Tampere, Finland, alongside Lawrence Clark on tenor saxophone, Greg Murphy on piano, and Joris Teepe on bass; it was released in 2009, shortly before Ali's death that August.

Evans released his debut album as a leader, Portrait (Snavesounds), on January 1, 2011. The ten-track session features Lawrence Clark and Raymond "Ray Mac" McMorrin on saxophones, pianists Alan Jay Palmer and Theo Hill, bassist Dezron Douglas, and drummer Ralph Peterson, and includes a version of "Ballad," a Rashied Ali composition, alongside seven Evans originals and two jazz standards. His second leader date, Hope And Despair (Passin' Thru Records), was recorded November 17-18, 2014, in Brooklyn and released in 2015; produced by Jahi Lake and Richard Franklin, with cover photography and artwork by saxophonist and visual artist Oliver Lake, it splits its personnel across two working bands, one with Lawrence Clark and Bruce Williams on saxophones and drummer Kush Abadey, the other with Abraham Burton on tenor and drummer Eric McPherson, plus pianist David Bryant and bassist Rashaan Carter throughout, all twelve tracks composed or arranged by Evans himself.

Through the 2010s and into the 2020s, Evans built a busy New York sideman career alongside his own leader dates. He has recorded and toured with pianist Orrin Evans's Captain Black Big Band (no relation, despite the shared surname), drummer Ralph Peterson's Unity Project, bassist Joris Teepe's own big band, the Joe Chambers Moving Pictures Orchestra, the Smalls Legacy Band, the Valery Ponomarev Big Band, and Christian McBride's New Jawn, appearing on that group's self-titled 2018 debut and 2023's Prime. He is a recurring member of vocalist Jazzmeia Horn's bands, appearing on A Social Call (2017), Love and Liberation (2019), and Dear Love (2021), and more recently joined the Black Art Jazz Collective for Truth To Power (2024, HighNote Records). On July 31, 2016, Evans premiered Mansa Mali, an evening-length suite for quintet, at the Museum of Modern Art's Sculpture Garden, with Keith Loftis on tenor saxophone and flute, David Bryant on piano, Rahsaan Carter on bass, and Kush Abadey on drums. Drawing on stories from the Mali Empire's Atlantic voyages and the astronomical traditions of the Dogon people, subjects McLean had introduced him to years earlier, Evans described the piece as his own "jazz interpretation," not an imitation of West African source material. He later documented a version of that project on the self-released CD Mansa; exact recording and release details are not confirmed beyond his own website.

Evans self-released a further run of leader recordings, including the "In The Tradition" series (Vols. 1 through 3), digital-only sessions drawing on a deep well of New York mainstream players including drummer Louis Hayes, saxophonists Joe Ford and Stacy Dillard, trombonist Frank Lacy, and vibraphonist Joel Ross; specific recording dates are not documented outside his own site. He continues to lead his own working Josh Evans Big Band, teaches trumpet, theory, composition, and arranging through online lessons, and remains active on New York's mainstream jazz scene, appearing as a sideman as recently as 2026 on bassist Corcoran Holt's Freedom of Art.

Evans plays in a modern mainstream idiom rooted in hard bop, and names Jackie McLean and Rashied Ali as the two biggest influences on his playing, an unusual pairing of a bebop-schooled alto saxophonist and a drummer best known for the most radical, form-dissolving phase of John Coltrane's career. His own leader albums, Portrait and Hope And Despair, sit closer to McLean's structured, blues-rooted hard bop than to Ali's free playing, but Evans has credited his time in Ali's working band with opening his sense of time and rhythmic freedom within otherwise conventional forms, an influence Lawrence Clark, his bandmate in that same Ali quintet, has described in near-identical terms about his own writing. Among living musicians, Evans has singled out pianist McCoy Tyner as the player he admires most for revolutionizing the instrument's harmonic conception, and cites vocalist Shirley Horn's elegant, unhurried phrasing as a specific influence on his own approach to melody. He has also credited trombonist Grachaan Moncur with early professional opportunities during lean periods of his career.