Founded by John Eliot Gardiner, the group regularly performs throughout England and Europe. It has given a number of concerts in two London halls, the Barbican and St. John's Smith Square. The English Baroque Soloists drew many of their original members from another group Gardiner had founded (in 1968), the Monteverdi Orchestra.

Shortly after their founding, Bach and Handel were largely the focus of the EBS. However, the EBS became closely associated with Mozart's music, mainly because of its numerous, generally highly acclaimed recordings of his works. In 1984, Gardiner and the EBS launched a series for the label Archiv Produktion devoted to Mozart's concertos for piano and orchestra with soloist Malcolm Bilson (using a fortepiano) and the first such cycle using period instruments. Two years later, with the concerto series ongoing, they launched another Mozart project, this one to cover the mature symphonies for Philips. In summer 1990, the EBS debuted at the Salzburg Festival, giving three concerts, all to critical acclaim.

With the release in 1990 of Piano Concerto No. 24, K. 491, and No. 27, K. 595, the piano concerto series was completed, but the EBS and Gardiner immediately set to work recording the seven mature operas of Mozart for Archiv Produktion. The first release in this cycle, Idomeneo, won Gramophone's Best Opera Award in 1991. In that same year. Gardiner, the EBS, and the Monteverdi Choir appeared in a live BBC television broadcast of Mozart's Requiem performed at the Palau de la Música Catalana. The last issue in the Gardiner/EBS Mozart operas series, Die Zauberflöte, was released in 1996, after which they turned to the music of Bach.

In the late 1990s, a new series of recordings began with the release in 2000 of Bach's Cantatas No. 6 "Bleib bei uns, denn es will Abend" (BWV 6) and No. 66, "Erfreut euch, ihr Herzen" (BWV 66). Along with the Monteverdi Choir, Gardiner and the EBS performed the entire cycle of 198 Bach cantatas throughout various European churches in 2000. But the EBS was hardly focusing on only Mozart or Bach in the 1990s: its performance at Covent Garden in 1995 of Haydn's Die Schöpfung (The Creation) was enthusiastically received and led to a successful 1997 recording on Archiv Produktion. Also in 1995, the EBS and the Monteverdi Choir performed the music for the film England, My England, a highly acclaimed movie directed by Tony Palmer, about English composer Henry Purcell. That same year, Gardiner, the EBS, and Monteverdi Choir issued a multi-disc set on the label Erato devoted to Purcell's music.