Richard Elliot was born in Glasgow, Scotland, on January 16, 1960, and moved with his family to Los Angeles at the age of three. His education in music started at home. His sister, ten years older, let him listen to her record collection on the condition that he put everything back where it belonged, and the shelf ran from Joni Mitchell, Carlos Santana and Dave Brubeck to Smokey Robinson, the Temptations and the Four Tops. He gravitated to R&B and the Motown sound, and as a teenager took up the tenor saxophone. At about eighteen he heard Dexter Gordon at Concerts by the Sea in Los Angeles and has described the experience as life changing, the moment he decided he would never come up with a sound that big. His first professional work, while still a teenager, was with Natalie Cole and the Pointer Sisters.

His earliest records were made in a different idiom from the one that later made him famous. He played saxophones and the lyricon, an electronic wind instrument, in Kittyhawk, a jazz-rock band whose lineup of Chapman Stick, cello, guitars and drums gave it an unusual texture; the band's self-titled debut came out in 1980. Elliot is also credited for lyricon and saxophone on the 1983 Yellowjackets album Mirage a Trois, and the Motown work his biography mentions is on record as well: saxophone and lyricon on a track of the Temptations' Surface Thrills (1983), and lyricon solos on Smokey Robinson's Smoke Signals (1986), where the Tower of Power horns also play.

In 1982 he joined the horn section of Tower of Power, the Oakland funk and soul band, and stayed until 1987, five years that he has said shaped his style; he plays alto and tenor saxophone and lyricon on the band's T.O.P. (1986) and Power (1987). His own career as a leader overlapped with that job: Initial Approach appeared on the small ITI label in 1984, and Trolltown (Intima, 1986) came out while he was still on the road with the band. When he left, the tenor chair went to Euge Groove, whom Elliot himself had recommended as his replacement.

Through the late 1980s he made records for Intima, an imprint under Enigma Records, among them The Power of Suggestion (1988), Take to the Skies (1989) and What's Inside (1990). Take to the Skies contains his cover of Percy Sledge's "When a Man Loves a Woman," a track often credited with launching his solo career. Bruce Lundvall signed him to Blue Note, and the Capitol-owned Manhattan and Blue Note imprints issued On the Town (1991), Soul Embrace (1993), After Dark (1994), City Speak (1996), Jumpin' Off (1997, on the Metro Blue imprint) and Chill Factor (1999). His official biography counts On the Town, Soul Embrace, After Dark and Jumpin' Off as No. 1 albums, and Chill Factor stayed on Billboard's contemporary jazz chart for more than 94 weeks. In the mid-1990s he helped start the Guitars & Saxes package tour, which also carried Peter White, Warren Hill and Craig Chaquico, and he joined the Groovin' for Grover and Jazz Attack tours, the former a tribute to Grover Washington Jr..

He moved to GRP and Verve for Crush (2001), on which keyboardist Jeff Lorber co-wrote and played on four tracks, and Ricochet (2003). In 2005 he and trumpeter Rick Braun founded the ARTizen Music Group, which issued his Metro Blue (June 28, 2005); its cover of the Stylistics' "People Make the World Go Round" spent eleven weeks at No. 1 on the Radio & Records airplay chart. Elliot and Braun made the duo album R n R (2007) and toured behind it. ARTizen became Artistry Music, distributed by Mack Avenue, and Elliot followed with Rock Steady (2009), a nod to the R&B of his youth, and In the Zone (October 2011), written and produced with Lorber to mark his twenty-fifth year as a recording artist.

In 2013 he joined Dave Koz, Gerald Albright and Mindi Abair on Summer Horns (Concord, May 7, 2013), a four-saxophone album that earned the one Grammy nomination of his career, for Best Pop Instrumental Album at the 56th Annual Grammy Awards. Elliot, Koz and Albright returned for Summer Horns II: From A to Z (Concord, 2018), with trumpeter Rick Braun and trombonist Aubrey Logan joining them. His own albums continued with Lip Service (Heads Up, 2014), Summer Madness (2016), Authentic Life (Shanachie, January 29, 2021), which brought in Braun, Koz, Lorber and others, and Straight Up Down (Shanachie, September 6, 2024), described by his own biography as his twenty-first recording as a leader, with Euge Groove producing two of its tracks.

Elliot lives in the San Diego area with his wife, Camella, and their five children. He is a licensed pilot, was building a two-seat airplane in his garage as of 2024, and once worked as a software engineer. He continues to tour; his 2026 dates included an appearance at the Tucson Jazz Festival on June 7.

Elliot is a smooth jazz and R&B instrumentalist first, and his own biography says as much: a soulful, bluesy approach that blends jazz, blues, pop, R&B and rock, with supple, agile tenor lines. The funk side comes from five years in Tower of Power's horn section, and the pop side from a steady line of covers, from "When a Man Loves a Woman" and "I'm Not in Love" to "People Make the World Go Round" and "Rock Steady." His records were made for the radio format that took shape as his solo career began, and he has more than twenty Top 10 smooth jazz singles to his name.

The jazz lineage he names is the tenor tradition: Dexter Gordon, Johnny Griffin, Gene Ammons, Coleman Hawkins, Grover Washington Jr. and Michael Brecker. For In the Zone he named Washington, Bob James and David Sanborn as the jazz-funk players he was saluting. The albums lean on session players such as Paul Jackson Jr. and Lenny Castro and on producers from the contemporary jazz scene, including Paul Brown, Steve Dubin and Jeff Lorber, and they are better understood as instrumental R&B with jazz soloing than as improvisation-led jazz. His long run on the contemporary jazz charts, and his place on the Summer Horns records beside Dave Koz and Gerald Albright, are what put him in the center of that world.