Costello was born Declan Patrick MacManus in St Mary's Hospital, Paddington in London, the son of Mary (née Costello) and Ross MacManus, a musician and bandleader. Costello lived in Twickenham, attending what is now St Mark's Catholic Secondary School in neighbouring Hounslow.

With a musically inclined father (his father sang with The Joe Loss Orchestra), Costello's first broadcast recording was alongside his dad in a television commercial for R. White's Lemonade ("I'm a Secret Lemonade Drinker"). His father wrote and sang the song; Costello provided backing vocals. The ad won a silver award at the 1974 International Advertising Festival.

Costello moved with his Liverpool-born mother to Birkenhead in 1971. It was there that he formed his first band, a folk duo called Rusty. After completing secondary school at St. Francis Xavier's College Liverpool, he moved back to London where he next formed a band called Flip City, which had a style very much in the pub rock vein. They were active from 1974 through early 1976. Around this time, Costello adopted the stage name D.P. Costello.

To support himself, he worked a number of office jobs, most famously at the Elizabeth Arden cosmetics firm – immortalised in the lyrics of "I'm Not Angry" as the "vanity factory" – where he worked as a data entry clerk. He worked for a short period as a computer operator at the Midland Bank computer centre in Bootle, Liverpool.

He continued to write songs, and began actively looking for a solo recording contract. On the basis of a demo tape, he was signed to noted independent label Stiff Records. His manager at Stiff, Jake Riviera, suggested a name change, using Elvis Presley's first name despite Costello having a small antipathy towards Presley, and Costello comes from his great grandmother's name to form Elvis Costello.

The first Costello single for Stiff was "Less Than Zero" b/w "Radio Sweetheart (single mix)", released on 25 March 1977. Two months later, Costello's first album, My Aim Is True (1977), was a moderate commercial success (No. 14 in the UK and Top 40 in the US) with Costello appearing on the cover in his trademark oversize glasses, bearing a striking resemblance to a menacing Buddy Holly.

A highlight of the album was the country-influenced ballad "Alison" with a typically biting Costello lyric. Costello's backing on this first album was provided by American West Coast band Clover, a roots/country outfit living in England (contrary to rumor, Clover did not exactly become Huey Lewis and the News - Huey Lewis did play with Clover shortly before the recording of My Aim Is True, but he and Sean Hopper, who appears on Costello's record, struck out on their own later). Costello was originally marketed as a punk artist. Later on, as the term New Wave was applied to the first post-punk bands, Costello was classified as new wave for a time.

The same year, Costello recruited via auditions his own permanent band, The Attractions, consisting of Steve Nieve (born Steve Nason; piano), Bruce Thomas (bass guitar), and Pete Thomas (drums; unrelated to Bruce Thomas). He released his first major hit single, "Watching the Detectives", which was recorded with Nieve and the pair of Steve Goulding (drums) and Andrew Bodnar (bass), both members of Graham Parker & The Rumour (whom he had used to audition for The Attractions).

Stiff's records were initially distributed only in the UK, which meant that Costello's first album and singles were initially available in the US as imports only. In an attempt to change this, Costello was arrested for busking outside of a London convention of CBS (Columbia Records) executives, "protesting" that no US record company had yet seen fit to release Elvis Costello records in the United States. Costello signed to CBS in the US a few months later.

In December 1977, Costello and The Attractions appeared on Saturday Night Live as a last minute fill-in for the Sex Pistols, but Costello ended up causing some controversy himself, and was banned from the program for over a decade. Following a whirlwind tour with other Stiff artists (captured on the Live Stiffs album, notable for Costello's recording of the Burt Bacharach/Hal David standard "I Just Don't Know What to Do With Myself") the band recorded the frenetic, raucous This Year's Model (1978).

Some of the more popular tracks include the British hit "(I Don't Want To Go To) Chelsea" and the subversively anthemic "Pump It Up". His U.S. record company saw Costello as such a priority that his last name replaced the word "Columbia" on the label of the disc's original pressing.

A tour of the US and Canada also saw the release of the much bootlegged promo-only "Live at the El Mocambo", which finally saw an official release as part of the "2½ Years" box set in 1993. It was during the ensuing United States tour that Elvis met and developed a relationship with former Playboy model, Bebe Buell (mother of Liv Tyler).

Their on-again-off-again courtship would last until 1984 and would allegedly become a deep well of inspiration for some of Costello's most lovelorn songs. 1979 would arguably see the peak of Costello's commercial success with the release of Armed Forces (originally to have been titled Emotional Fascism, a phrase that appeared on the LP's inner sleeve).

Both the album and the single Oliver's Army went to #2 in the UK. Costello also found time in 1979 to produce the debut album for 2 Tone ska revival band, The Specials.