Herb Alpert was born Herbert Alpert on March 31, 1935, in Los Angeles and grew up in Boyle Heights, the youngest of three children of Jewish immigrants from Eastern Europe. His father was a tailor who played mandolin, his mother taught violin, his older brother David was a drummer and his sister Mimi played piano. He took up the trumpet at eight, attended Fairfax High School, played two years in the University of Southern California marching band and served in the Army during the Korean War, where he was in the 6th Army Band. In 1956 he appeared as an uncredited drummer in Cecil B. DeMille's The Ten Commandments.

His first foothold in music was as a songwriter. In 1957 he teamed with Lou Adler at Keen Records, and songs written or co-written by the pair over the next two years included "Baby Talk" for Jan and Dean and "Wonderful World" for Sam Cooke. In 1960 he began recording as a vocalist for RCA under the name Dore Alpert. In 1962 he and Jerry Moss formed a label called Carnival Records, found the name already taken and renamed it A&M, after their initials. Alpert has said that the trumpeters he first imitated were Harry James, Louis Armstrong, Miles Davis and Clifford Brown, and that he found his own voice around 1958, after hearing Les Paul and Mary Ford's "How High the Moon," where Les Paul layered several guitar parts. Alpert applied the same overdubbing idea to the trumpet, using two tape machines, and that sound became the Tijuana Brass.

The first record was "The Lonely Bull," adapted from a tune called "Twinkle Star" after Alpert attended a bullfight in Tijuana and added crowd noise and a mariachi-style trumpet call. He paid for the single himself, radio disc jockeys spread it, and in the fall of 1962 it reached No. 6 on the Billboard Hot 100. The album The Lonely Bull was A&M's first and reached No. 10 on the Billboard 200. On this and the following records Alpert worked with Los Angeles session players later known as the Wrecking Crew, whom he still holds in high regard. Whipped Cream & Other Delights (1965), with its cover photograph of a model covered in what he later said was shaving cream, spent eight weeks at No. 1 beginning November 27, 1965, and was the number-one album of 1966. By then the Tijuana Brass had to become a touring band, and in one week of May 1966 five of its albums sat in the Billboard top 20. At the 8th Grammy Awards in 1966, "A Taste of Honey" won Record of the Year, Best Instrumental Performance and Best Instrumental Arrangement. "This Guy's in Love with You," a Burt Bacharach and Hal David song that Alpert sang on a 1968 CBS special, became A&M's first No. 1 single, and it remains a rare vocal in his catalog. The decade's pop side included the band's recording of the Bacharach title theme for the film Casino Royale (1967) while "Tijuana Taxi" and "Spanish Flea" are the two songs in a John and Faith Hubley animated short that won the Academy Award for Best Animated Short Film in 1967.

In 1969 Alpert reached a personal crisis in which he declared the trumpet his enemy. He disbanded the Tijuana Brass and stopped performing in public. He studied with the teacher Carmine Caruso and came back with You Smile - The Song Begins (1974), arranged by Quincy Jones and with the pianist Dave Frishberg, guitarist John Pisano and drummer Nick Ceroli. AllMusic's Richard S. Ginell heard a trumpet that sounded more soulful and thoughtful, and an artist whose ears were more attuned to jazz than ever. The same album includes Chuck Mangione's "Legend of the One-Eyed Sailor" and a version of Gato Barbieri's "Last Tango in Paris," which had reached No. 77 on the Hot 100 as a single the year before.

The late 1970s brought two separate peaks. Herb Alpert / Hugh Masekela (1978), made with the South African trumpeter Hugh Masekela and released on A&M and its jazz imprint Horizon, was followed by the live Main Event Live. Then "Rise," written by Andy Armer and Alpert's nephew Randy Alpert, spread through club play and the television soap opera General Hospital and reached No. 1 on the Hot 100 in October 1979. That made Alpert the only musician to top the Hot 100 both as a vocalist and as an instrumentalist. The Rise album reached No. 6 on the Billboard 200 and No. 1 on the Billboard jazz albums chart, and its title track won the 1980 Grammy for Best Pop Instrumental Performance. In 1987 he returned to the top five of the Hot 100 with "Diamonds," recorded with Janet Jackson and Lisa Keith for his album Keep Your Eye on Me. A&M had become the world's largest independent record company within a decade of its founding, and its artists over the years included Sergio Mendes and Brasil '66, the Carpenters, Chuck Mangione, Quincy Jones, Wes Montgomery and the Police. In 1989 Alpert and Moss sold it to PolyGram, which announced the $500 million purchase on October 11 of that year. Moss passed away in August 2023.

From the 1990s the records lean toward the jazz side. Midnight Sun (A&M, 1992) is an album of late-night standards that includes two vocals by Alpert and a duet with Stan Getz recorded in 1990, with Larry Carlton on guitar, Harvey Mason on drums and Monty Budwig on bass on most tracks. After A&M he and Moss started Almo Sounds, where Alpert made Second Wind (1996), Passion Dance (1997) and Colors (1999), all of which charted on Billboard's jazz albums chart. In 2004 he and his daughter Eden opened Vibrato Grill & Jazz, a jazz club and restaurant in Bel Air. He recorded with his wife, the singer Lani Hall, on Anything Goes (Concord Jazz, 2009), I Feel You (Concord Jazz, 2011) and Steppin' Out (2013), which won the Grammy for Best Pop Instrumental Album in January 2014. Since 2015 his albums have appeared on his own Herb Alpert Presents label, and Over the Rainbow (2019) debuted at No. 1 on Billboard's Contemporary Jazz Albums chart dated October 5, 2019. A documentary, Herb Alpert Is..., appeared in 2020. His 50th studio album, 50, came out on September 20, 2024, followed by the holiday album Christmas Time Is Here in 2025.

Alpert is also one of the most active arts philanthropists in the United States. He created the Herb Alpert Foundation in the 1980s, and it has supported the Alpert Awards in the Arts at CalArts, the Harlem School of the Arts (whose building was renamed the Herb Alpert Center in 2013) and a $10.1 million gift in 2016 that made music study at Los Angeles City College tuition-free. In 2007 he and Lani Hall gave $30 million to UCLA, which named its Herb Alpert School of Music. The ASCAP Foundation's Herb Alpert Young Jazz Composer Awards carry his name and are funded by his foundation. He is a painter and sculptor, was inducted into the Rock and Roll Hall of Fame with Moss in 2006 as a nonperformer, received the Recording Academy Trustees Award with Moss in 1997 and was presented the National Medal of Arts at the White House in July 2013. Grammy.com lists eight Grammy wins and 24 nominations.

At age 91 he remains active. In late 2024 he formed a new Tijuana Brass to celebrate the 60th anniversary of Whipped Cream & Other Delights, and that band has toured through 2026, with dates scheduled into 2027.

Alpert's career is best described in three layers, and the profile is clear about which is which. The Tijuana Brass records of 1962 to 1969 are instrumental pop, with mariachi trumpet calls, Latin rhythms and arrangements of show tunes and standards, and they are better filed under easy listening than under jazz. The business side is real and large: he co-founded and ran A&M Records and was never merely a performer. The jazz side is smaller and documented. He names Harry James, Louis Armstrong, Miles Davis and Clifford Brown as his own models, he made a standards album with Stan Getz and Larry Carlton on it, several albums from Rise onward reached Billboard's jazz charts and Over the Rainbow went to No. 1 on its contemporary jazz chart, he has recorded for Concord Jazz, and Wikipedia files him among American jazz trumpeters, jazz bandleaders and smooth jazz trumpeters.

As a player he is a melodic, ballad-oriented trumpeter rather than a bebop technician. Alpert has said that the real instrument is the player's feelings and not the lip or the technique, and the 1974 comeback was heard as the point where that approach turned toward jazz. The multitrack trumpet he built from Les Paul's example is the one distinctive technical idea in the early records. As a label head his taste ran wider than his own sound. A&M carried Brazilian and Latin acts, the CTI jazz line under Creed Taylor from 1967, and from 1974 to 1978 the Horizon imprint, which issued records by Ornette Coleman, Charlie Haden, Jim Hall, Paul Desmond and Dave Brubeck.