Alois Maxwell Hirt was born in New Orleans on November 7, 1922, the son of a police officer. He was given his first trumpet at six, bought at a pawnshop, and played in the city's Junior Police Band. By sixteen he was working professionally, often alongside his friend Pete Fountain while still a student at Jesuit High School, and a job playing at the local racetrack began a connection to horse racing that lasted six decades. In 1940 he went to Cincinnati to study at the Cincinnati Conservatory of Music with Frank Simon, a former soloist with John Philip Sousa's band. After service as an Army bugler in World War II he played in swing big bands, among them those of Tommy Dorsey, Jimmy Dorsey, Benny Goodman and Ina Ray Hutton; AllMusic's Scott Yanow also lists Ray McKinley. In 1950 he became first trumpet and featured soloist with Horace Heidt's orchestra, and after several years on the road he came home to New Orleans to lead his own bands and work with Dixieland groups.

Hirt disclaimed the jazz label. He said later that he was not a jazz trumpeter and never had been, yet his New Orleans records of the 1950s are Dixieland jazz: sessions with the bandleader Monk Hazel, albums for the local Southland label, and the Audio Fidelity series Swingin' Dixie, recorded at Dan's Pier 600 on Bourbon Street. From the mid-1950s to the early 1960s his band played there nightly, in a club owned by his business manager Dan Levy Sr., and for a time he co-led the band with Fountain. In 1962 he opened his own room, Basin Street South, on Bourbon Street in the French Quarter, which stayed open until 1983.

RCA Victor signed him, and the label turned a fast, brilliant trumpeter into a pop star. He placed twenty-two albums on the Billboard charts in the 1950s and 1960s. Honey in the Horn (1963), produced by Chet Atkins and Steve Sholes with Nashville session players, reached No. 3, and its single "Java," an Allen Toussaint tune, climbed to No. 4 on the Billboard Hot 100 on February 29, 1964 and spent four weeks at No. 1 on the easy listening chart. Cotton Candy and Sugar Lips followed in 1964, reaching No. 6 and No. 9 on the album chart, with the title tracks at No. 15 and No. 30 on the Hot 100. Both Honey in the Horn and "Java" sold more than a million copies and earned gold discs. At the 6th Annual Grammy Awards, held May 12, 1964, "Java" won the award for Best Performance by an Orchestra or Instrumentalist with Orchestra, Not for Jazz or Dancing. The same ceremony nominated Honey in the Horn for Album of the Year and nominated Our Man in New Orleans, his Dixieland set arranged by Marty Paich, in both of that year's instrumental jazz performance categories. Over his lifetime he received eight Grammy nominations.

The television and film work followed from the hits. "Sugar Lips" became the theme of the NBC game show Eye Guess, which aired from 1966 to 1969, and Hirt recorded the "Green Hornet Theme," Billy May's arrangement of Rimsky-Korsakov's "Flight of the Bumblebee," for the television series; the recording reached a new audience in the 2003 film Kill Bill. He appeared in the 1962 feature Rome Adventure, hosted the CBS summer series Fanfare in 1965, and became a minority owner of the NFL's New Orleans Saints in 1967. On January 11, 1970 he performed at the Super Bowl IV halftime show alongside Marguerite Piazza, Lionel Hampton, Doc Severinsen and the Southern University marching band. In 1986 he joined Sarah Vaughan, Dizzy Gillespie, Chuck Mangione, Don Cherry and Maynard Ferguson for a televised jazz session in New Orleans, and in 1987 he played "Ave Maria" for Pope John Paul II's visit to the city.

On February 8, 1970, riding a float in a Mardi Gras parade, Hirt was hurt in the mouth and needed twelve stitches inside his upper lip. It was widely reported that he had been hit by a thrown brick or piece of concrete, but the cause rests mainly on his own account, and police described that year's Mardi Gras as unusually rough. He had surgery and returned to the club circuit. Saturday Night Live later parodied the story with a contest called "Let's Hit Al Hirt in the Mouth with a Brick."

He stayed a New Orleans fixture to the end. When Wynton Marsalis was six, Hirt, sitting at a table with the boy's father and other trumpeters, offered to give him his first trumpet. Hirt spent his last year in a wheelchair because of swelling in his leg, and he passed away in New Orleans on April 27, 1999, at 76, of liver failure. His wife Beverly Essel Hirt and eight children from an earlier marriage survived him. The Louisiana Music Hall of Fame inducted him in November 2009.

Hirt was a big-toned, fast-fingered trumpeter with a wide range and a classical background, and the critics who admired his technique were often the ones who wished he had used it differently. Scott Yanow wrote that he was frequently overqualified for the Dixieland and pop material he played, that he tended to play far too many notes, and that his early Audio Fidelity recordings of 1958 to 1960 and his collaborations with Fountain are the most rewarding of his career. Yanow names Harry James as an influence, and the swing era shows in his phrasing. His first RCA Victor album, He's the King (1961), mixes Dixieland and swing repertoire, including "Jazz Me Blues," "One O'Clock Jump" and Louis Armstrong's "Cornet Chop Suey."

Most of the records that made him famous are instrumental pop, and they are described that way here. The Nashville-built Honey in the Horn, Cotton Candy and Sugar Lips wrap the trumpet in Anita Kerr's vocal group and a Music Row rhythm section; Horn A-Plenty (1962) puts him in front of a Billy May big band playing standards and show tunes; later RCA albums include Latin and soul sets and a Bert Kaempfert tribute, and in the 1970s he recorded for the Nashville label Monument. The Grammy category that rewarded "Java" was literally labeled as not for jazz or dancing. The jazz side is real but runs through Dixieland: the New Orleans club sets, the Fountain collaborations, Our Man in New Orleans, and the 1986 session with Dizzy Gillespie, Chuck Mangione and Don Cherry. Among the early-1960s instrumental hitmakers, Herb Alpert and Acker Bilk are the closest comparisons, and AllMusic lists Alpert as a related artist.