Backed by a Dutch millionaire named Stanley August Miesegaes, vocalist, pianist and ex-drummer Rick Davies (born Richard Davies, July 22, 1944 in Eastcott Hill, Swindon, Wiltshire, England) used newspaper advertising in Melody Maker to recruit an early version of the band in August 1969, an effort which recruited vocalist/guitarist and keyboardist Roger Hodgson (born Charles Roger Pomfret Hodgson, March 21, 1950 in Portsmouth, Hampshire, England). Other members of this proto-Supertramp included Richard Palmer (guitar, balalaika, vocals) (born Richard Jeffrey Charles Palmer-James, 11 June 1947, in Bournemouth, Dorset) and Robert Millar (percussion, harmonica) (born 2 February 1950). Initially, Roger Hodgson sang and played bass guitar (and, on the side, guitar, cello and flageolet). The band was called Daddy from August 1969 to January 1970, at which time this was changed to Supertramp, a name taken from W.H. Davies' book, The Autobiography of a Super-Tramp, published in 1908.

They were one of the first groups to be signed to the UK branch of A&M Records. The first album, Supertramp, was released in July 14, 1970 in the UK and Canada only (it was first issued in the US in 1977). Although it was very intense and lyrical, it proved not to attract the audience and little of critics paid any attention to this first effort. However, Supertramp was able to earn a slot on the bill of the 1970 Isle of Wight Festival, which was headlined by the likes of The Doors, The Who, and Jimi Hendrix. Richard Palmer abruptly quit six months after the album's release. Robert Millar suffered a nervous breakdown shortly afterwards. For the next album, Indelibly Stamped, released in June 1971 (in both UK and US), Frank Farrell (bass) (born in 1947 in Birmingham, West Midlands), Kevin Currie (percussion) (born in Liverpool, Merseyside) and Dave Winthrop (flute and saxophone) (born 27 November 1948, in New Jersey, USA) replaced Millar and Palmer, while Roger Hodgson switched to guitar. "Indelibly Stamped" featured rocking Beatlesque tunes, with vocal harmonies similar to Simon and Garfunkel songs (Davies now serving as the band's second lead singer, alongside Hodgson, who suggested that the band should have two lead vocalists), a more commercial approach and eye-catching cover artwork. Supertramp had established themselves as a "cult" band. Sales, however, failed to improve and sold even less than their debut. In early 1972, Miesegaes withdrew his support from the band after paying off debts. All members gradually quit except Hodgson and Davies.

These two first albums were later reissued during Supertramp's popularity peak and have maintained a certain appeal with die-hard fans. The first album is melancholic and quieter and the songs are spread out more than they were later on. Roger Hodgson once called it his favourite Supertramp album (which later became Crime of the Century). The second album is their most traditionally rock album, and certainly their heaviest sound.

In late 1972, after being persuaded to carry on, Davies and Hodgson went on an extensive search for replacements, which first brought aboard Dougie Thomson (born Douglas Campbell Thomson, March 24, 1951 in Rutherglen, Glasgow, Strathclyde, Scotland) (bass), who played with the band almost a year before auditions resumed to complete the line-up. In 1973, auditions restarted and brought in Bob Siebenberg (born Robert Layne Siebenberg, October 31, 1949 in Glendale, California, USA, drums, and credited for several years as Bob C. Benberg, the story goes, to stay under the radar of British Immigration), and John Helliwell (born John Anthony Helliwell, February 15, 1945 in Todmorden, Yorkshire, England) (saxophone, other woodwinds, occasional keyboards, backing vocals), joining original members Davies and Hodgson and the newly brought in Thomson, completing the line-up that would create the group's defining albums. Hodgson would also begin playing keyboards in the band in addition to guitar, usually acoustic and electric pianos on his own compositions. The classic Supertramp keyboard is a Wurlitzer electric piano (model 200A) with its unmistakable bright sound and biting distortion when played hard.

Crime of the Century, released in September 1974, began the group's run of critical and commercial successes, hitting number four in Britain, supported by the iconic countercultural opening track "School", and the top-10 single "Dreamer". Its B-side "Bloody Well Right" hit the US Top 40 in May 1975. Siebenberg would later comment that he thought the band hit its artistic peak on this, their third album, though their greatest commercial success would come later.

The band continued with Crisis? What Crisis? released in November 1975. It achieved good though not overwhelming commercial success. The following album, Even in the Quietest Moments, released in April 1977 spawned their hit single Give a Little Bit, and the FM radio staple Fool's Overture. During this period, the band eventually relocated to the United States and moved steadily from the progressive styles of their early albums towards a more song-oriented pop sound.

This trend reached its zenith on their most popular album, Breakfast in America in March 1979, which reached Number 3 in the UK and Number 1 in the United States and spawned four successful singles, "The Logical Song", "Take the Long Way Home", "Goodbye Stranger" and "Breakfast in America". The album has since sold over 18 million copies worldwide.

The run of successes was capped with 1980s Paris, a 2-LP live album, in which the band stated its goal of improving on the studio versions of their songs. Instead of focusing on songs from the hugely successful Breakfast in America, it included nearly every song from Crime of the Century, another testament to the importance of that album in the group's development. Initially, it was supposed to be a show recorded in Quebec City, Canada, but A&M vetoed the idea for a "more mainstream city".