George Onslow was born in Clermont-Ferrand, the son of an English father, Edward Onslow, and a French mother, Marie Rosalie de Bourdeilles de Brantôme; his paternal grandfather was George Onslow, 1st Earl of Onslow. In Onslow's own brief autobiography (written in the third person) he comments that in his childhood, "music studies formed but a secondary part of his education" but names Jan Ladislav Dussek and Johann Baptist Cramer amongst his piano teachers. It has been suggested that he received this tuition in London under the aegis of his grandfather the Earl. However, other research indicates he may not have studied with Dussek until 1797–1798 in Hamburg, where his family was living in exile after his father had become involved in counter-revolutionary activities in France. This research also indicates there is no evidence to support the suggestions sometimes made that Onslow at any time visited Vienna, or that he met, or studied, there with Ludwig van Beethoven.
Onslow states in his autobiography that his attitude to music was transformed by his experience of hearing the overture to Étienne Méhul's opera Stratonice in Paris in 1801. In Onslow's own later words "On hearing this piece, I experienced so lively an emotion in the depths of my soul that I sensed myself at once penetrated by feelings previously unknown to me; even today this moment is present in my thought. After this, I saw music with other eyes; the veil which had hidden its beauties from me was rent; it became the source of my most intimate joy, and the faithful companion of my life." This led him to compose his first string quintets (Op. 1 nos. 1–3) and string quartets (Op. 4 nos. 1–3), although he had not at this stage received any composition tuition. These were published at his own expense; Onslow was always wealthy and did not need critical or financial support. The critic François-Joseph Fétis noted that, despite his absence of training, Onslow "had all the leisure necessary to overcome these obstacles". Onslow learnt to play the cello, and to play the chamber music of Mozart, Haydn and Beethoven with other local amateurs. However, aware of the need to develop his technical musical skills, in 1808 he began to study composition with Anton Reicha in Paris. At this time he also married a French heiress, Charlotte Françoise Delphine de Fontanges, by whom he was to have three children.
Château de Bellerives, Pérignat (demolished 1990), on an old postcard
Onslow based himself near Clermont-Ferrand, initially at his father's Château de Chalendrat at Mirefleurs (where at the age of six he had planted many of the trees), later at Château de Bellerives at Perignat, La Roche-Noire. He typically visited Paris during the winter (concert) season, when his works were often performed, by musicians including the violinists Pierre Baillot and Théophile Tilmant, and the brothers Dancla, who gave quartet concerts. In 1824 and 1827 his first two operas, L'Alcalde de la vega and Le colporteur, were premiered at the Théâtre Feydeau in Paris under the auspices of the Opéra-Comique. Le colporteur was also produced in Germany, and even (in a very mangled version, in 1831), in London. In 1825 in Paris he met the 16-year-old Felix Mendelssohn, who enjoyed a performance of one of Onslow's quartets but was surprised that he was not aware of Beethoven's opera Fidelio. Onslow was an early enthusiast of the music of Hector Berlioz, whose Eight scenes from Faust (1829) and overture Les francs-juges (1830) he praised. In 1829, after Onslow had commenced his quintet op. 38 (his fifteenth), he was very seriously wounded in a hunting accident, which left him partially deaf in one ear; completing the quintet in the aftermath, he named the final movements "Fever", "Convalescence" and "Recovery". The work was subtitled "De la Balle" ("The Bullet").
Throughout the 1820s, Onslow's reputation continued to grow both in France and abroad as a series of trios, quartets and quintets were published. Onslow's publishers in Paris were Ignaz and Camille Pleyel. In 1818 his works began to be published in Germany by Breitkopf und Härtel and in Austria by C. F. Peters; the same year saw the first writings about his works by German music critics. Other German publishers, including Hoffmeister, Steiner and Simrock, followed in later years. In the 1830s, Onslow's quartets were in the repertoire of the Müller Quartet, which played them at the Meiningen court of Duke Bernhard II, and of the Prague-based quartet of Friedrich Pixis the younger.
In 1831 Onslow was elected the second Honorary Fellow of the Philharmonic Society of London (Felix Mendelssohn had been the first). He wrote for the Society his Second Symphony, Op. 42, and continued to maintain close relations with leading London musicians including John Ella and George Frederick Anderson. In 1834, Frédéric Chopin and Franz Liszt played Onslow's Grand Sonata for four hands Op. 22 at their debut joint performance in Paris. From 1835 to 1838 Onslow was the President of the Athenée musical in Paris, an association founded in 1829 "to propagate the study and the spirit of music", with the intention of bringing together both amateurs and professionals. 1837 saw the premiere in Paris of Onslow's third (and last) opera Le duc de Guise. In 1839 Onslow founded the "Société Philharmonique de Clermont" in which the émigré Polish violinist Alexandre Tarnowski was very active. Performances were given of Onslow's own chamber music, and also of his opera Guise, including passages which had been cut from the Paris performances. At the instigation of Tarnowski Onslow also hosted in Clermont-Ferrand the Polish-Jewish xylophonist and rival of Josef Gusikov, Sankson Jakubowski.
In 1842 Onslow's wealth increased on the death of his father-in-law, who owned extensive property. In the same year his French musical prestige was consolidated when he succeeded Luigi Cherubini as a member of the Académie des Beaux-Arts. Invited to the Aachen music festival in 1846, in the following year, on what may have been his last journey outside France, Onslow conducted his Fourth Symphony in Cologne, at the Niederrheinisches Musikfest. During his last years he wrote a number of pieces for large chamber ensemble with piano, including quintets, a sextet (Op. 77b) and a septet (Op. 79); he also wrote a nonet (op. 77a) for strings and woodwind. Onslow died unexpectedly (although after a period of declining health) in Clermont-Ferrand in 1853, after taking a morning walk.