On 25 January 1977, The Clash signed to CBS Records for £100,000, a remarkable amount for a band that had played a total of about thirty gigs and almost none as a headliner. As Clash historian Marcus Gray describes, the "band members found themselves having to justify [the deal] to both the music press and to fans who picked up on the critics' muttered asides about The Clash having 'sold out' to the establishment."

Mark Perry, founder of the leading London punk periodical, Sniffin' Glue, let loose with what he would later call his "big quote": "Punk died the day The Clash signed to CBS."

Mickey Foote, who worked as a technician at their concerts, was hired to produce The Clash's debut album, and Terry Chimes was drafted back for the recording. The band's first single, "White Riot", was released in March; the album, The Clash, came out the following month.

Filled with fiery punk tracks, it also presaged the many eclectic turns the band would take with its cover of the reggae song "Police and Thieves". Though both the single and album charted well in the UK—"White Riot" reached number 34, The Clash number 12—CBS refused to release either in the United States, saying that the sound was not “radio friendly”.

A US version of the album with a modified track listing was released in 1979, after the UK original became the best-selling import album of all time in the United States. Chimes left the band again soon after the recording, so only Simonon, Jones and Strummer were featured on the album's cover, and Chimes was credited as "Tory Crimes".

In the documentary Westway to the World, Jones referred to him as one of "the best drummers around". Chimes, who had no great wish to make a career from music, said, "The point was that I wanted one kind of life—they wanted another, and why are we working together, if we want completely different things?"

The band went through several drummers, with Jones handling the duties for a time. They finally recruited Nicky Headon, who had played briefly with Jones's London SS two years before. Headon was nicknamed "Topper" by Simonon, who felt he resembled the Topper comic book character Mickey the Monkey.

An excellent musician, Headon could also play piano, bass and guitar. He originally planned to stay briefly, gain a name for himself, and then find a better band. Realizing The Clash's potential, he changed his plans. In Westway To The World, Strummer noted, "If we hadn't found Topper, I don't think we'd have got anywhere".

Headon's first recording with the band was the single "Complete Control"; it was produced by famed reggae artist Lee "Scratch" Perry, but the result was pure punk rock. Released in September 1977, it rose to number 28 on the British chart and has gone on to be cited as one of punk's greatest singles. During this period, members of The Clash were arrested for various misdemeanors ranging from vandalism to the stealing of a pillowcase.

In February 1978, the band came out with the single "Clash City Rockers". June saw the release of "(White Man) in Hammersmith Palais", which surprised fans with its ska rhythm and arrangement. Before The Clash began recording their second album, CBS requested that they adopt a cleaner sound than its predecessor in order to reach American audiences.

Sandy Pearlman, known for his work with Blue Öyster Cult, was hired to produce the record. Although some complained about its relatively mainstream production style, Give 'Em Enough Rope received largely positive reviews upon its November release. It hit number 2 in the UK, but it was not the American breakthrough CBS had hoped for, reaching only number 128 on the Billboard chart. The album's first UK single, the hard rocking "Tommy Gun", rose to number 19, the highest chart position for a Clash single to date. In support of the album, the band undertook its first, largely successful tour of the US.

In August and September 1979, The Clash recorded London Calling. Produced by Guy Stevens, who had previously worked with Mott the Hoople and others, the double album was a mix of punk rock, reggae, ska, rockabilly, traditional rock and roll and other elements possessed of an energy that had hardly flagged since the band's early days, but with greater maturity and production polish.

It is regarded as one of the greatest rock albums ever recorded. London Calling reached number 9 on the British chart and number 27 on the US chart. Its final track, a relatively straightforward rock and roll number sung by Mick Jones called "Train in Vain", was included at the last minute and thus did not appear in the track listing on the cover.

It turned out to be the band's biggest US hit to date, reaching number 23 on the Billboard chart. In the UK, where "Train in Vain" was not released as a single, London Calling's title track, stately in beat but unmistakably punk in message and tone, rose to number 11—the highest position any Clash single reached in the UK before the band's breakup.

The Clash planned to record and release a single every month in 1980. CBS balked at this idea, and the band came out with only one single—an original reggae tune, "Bankrobber", in August—before the December release of the 3-LP, 36-song Sandinista!. The album again reflected a broad range of musical styles, including extended dubs and the first forays into rap by a major rock band.

Produced by the band members with the participation of Jamaican reggae artist Mikey Dread, Sandinista! was their most controversial album to date, both politically and musically. Critical opinion was divided, often within individual reviews. Trouser Press's Ira Robbins described half the album as "great", half as "nonsense" and worse.

In the New Rolling Stone Record Guide, leading critic Dave Marsh argued, "Sandinista! is nonsensically cluttered. Or rather seems nonsensically cluttered. One of the Clash's principal concerns...is to avoid being stereotyped." The album fared well in America, charting at number 24, even though it had no catchy single and, in the increasingly conservative environment of album-oriented rock (AOR) radio in the US, received minimal airplay.

During 1981, the band came out with a single, "This Is Radio Clash", that further demonstrated their ability to mix diverse influences such as dub and hip hop. They set to work on their fifth album in the fall, originally planning it as a 2-LP set with the title Rat Patrol from Fort Bragg.

Mick Jones produced one cut, but the other members were dissatisfied. Production duties were handed to Glyn Johns, and the album was reconceived as a single LP. Though Combat Rock was filled with offbeat songs, experiments with sound collage, and a spoken word vocal by Beat poet Allen Ginsberg, it contained two "radio friendly" tracks.

The leadoff single in the US was "Should I Stay or Should I Go", released in June 1982. Another Jones feature in a rock and roll style similar to "Train in Vain", it received heavy airplay on AOR stations. The follow-up, "Rock the Casbah", put lyrics addressing the Iranian clampdown on imports of Western music to a bouncy dance rhythm. (The singles were released in the opposite order in the UK, where they were both preceded by "Know Your Rights".)

The music for "Rock the Casbah" was composed by Headon, who performed not only the percussion but also the piano and bass heard on the recorded version. It was the band's biggest US hit ever, charting at number 8, and the video was put into heavy rotation by MTV. The album itself was the band's most successful, hitting number 2 in the UK and number 7 in the US.

After Combat Rock, The Clash began to disintegrate. Topper Headon was asked to leave the band just prior to the release of the album, due to his heroin addiction, which was hurting his health and drumming. The band's original drummer, Terry Chimes, was brought back for the next few months.

The loss of Headon, well-liked by the others, exposed the growing frictions within the band. Jones and Strummer began to feud. The band opened for The Who on a leg of their final tour in the US, playing (among other places) New York's Shea Stadium. Though The Clash continued to tour, the personal tensions were increasing.

In 1983, Chimes left the band after the end of the Combat Rock Tour, due to the in-fighting and turmoil. He was replaced by Pete Howard for the US Festival in San Bernardino, California, which The Clash co-headlined, along with David Bowie and Van Halen.

The crowd of roughly half a million was by far the biggest of The Clash's career. This was Jones's last appearance with the group. In September 1983, he was fired. The following year, he played guest guitar on the debut album by General Public.

Nick Sheppard, formerly of the Bristol-based Cortinas, and Vince White were selected as The Clash's new guitarists. Howard continued as the drummer. The reconstituted band played its first shows in January 1984 with a batch of new material and launched into the self-financed Out of Control Tour, traveling widely over the winter and into early summer.

At a striking miners' benefit show ("Scargill's Christmas Party") in December 1984, they announced that a new record would be released early in the new year.