Stéphane Grappelli was born January 26, 1908, at the Hôpital Lariboisière in Paris, the son of Ernesto Grappelli, an Italian-born scholar and translator from Alatri, and Anna Emilie Hanoque, who died when he was five. His father was drafted into the Italian army in 1914, and the young Grappelli was briefly enrolled at Isadora Duncan's Paris dance school before spending several harsh years in a Catholic orphanage until his father's return in 1918; he was naturalized as a French citizen the following year. He took up the violin at twelve, largely teaching himself, and studied at the Paris Conservatoire during the 1920s, graduating with a second-tier medal. At fifteen he began busking on the streets, then worked accompanying silent films in cinema pit orchestras. He discovered American jazz through records played at a Paris brasserie, and a 1928 Paris concert by the touring American jazz violinist Joe Venuti convinced him the violin could carry a genuine jazz solo voice.

In the early 1930s Grappelli met the guitarist Django Reinhardt, and the two began jamming together in Paris. In the summer of 1934 they formalized a group at the Hôtel Claridge on the Champs-Élysées: the Quintette du Hot Club de France, an unusual all-string lineup pairing Grappelli's violin and Reinhardt's lead guitar with rhythm guitarists Joseph Reinhardt and Roger Chaput and bassist Louis Vola. The quintet's first commercial release, "Dinah" backed with "Lady Be Good," was cut for Ultraphone in Paris on December 28, 1934 (the label misspelled both men's names). Over the rest of the decade the group toured Britain and the Continent and recorded prolifically, becoming Europe's most celebrated jazz act and giving jazz violin its first fully idiomatic voice. The partnership ended when war broke out in September 1939 while the quintet was on a London engagement.

Reinhardt returned to occupied Paris, but Grappelli chose to remain in England for the duration of the war, leading a new band that briefly included a young pianist named George Shearing, who made his own recording debut as a sideman in Grappelli's group. Grappelli and Reinhardt reunited on record intermittently after 1946, including a final run of sessions cut in Rome in January and February 1949 with pianist Gianni Safred, bassist Carlo Pecori and drummer Aurelio De Carolis, but the two never resumed a steady working partnership; Reinhardt died in 1953. Grappelli spent the 1950s and much of the 1960s working steadily in European clubs, including a long residency at Le Toit de Paris atop the Paris Hilton from 1967 to 1972, largely out of the American jazz press's view. Two sessions from that quieter stretch stand out: a September 1966 four-violin meeting in Basel with Stuff Smith, Svend Asmussen and Jean-Luc Ponty, released as Violin-Summit, and a February 1963 Paris date with members of Duke Ellington's orchestra, trumpeter and violinist Ray Nance among them, that was not issued until 1976 as Duke Ellington's Jazz Violin Session.

His career turned decisively in 1971, when a chance duet with the classical violinist Yehudi Menuhin on Michael Parkinson's British television talk show drew wide new attention; the two went on to record together intermittently between 1972 and the mid-1980s. In 1973 the guitarist Diz Disley persuaded Grappelli to return to the acoustic Hot Club instrumentation, and an ecstatic response at that year's Cambridge Folk Festival launched two decades of steady international touring, first with the Diz Disley Trio and later with guitarist Marc Fosset's groups. The revival brought a run of new studio partnerships: a violin-vibraphone duo album with Gary Burton, Paris Encounter (recorded 1969, released 1972 on Atlantic); a quintet session with fellow violinist Jean-Luc Ponty and guitarist Philip Catherine, Ponty-Grappelli (1974); Young Django (1979), pairing him with guitarists Larry Coryell and Philip Catherine; and a live album with mandolinist David Grisman drawn from their 1979 concerts in San Francisco and Boston, released in 1981.

Grappelli also worked steadily in film and on other artists' records during these decades. He composed the scores for Les Valseuses (1974) and Milou en Mai (1990), made cameo screen appearances including King of the Gypsies (1978, alongside Grisman) and an episode of Little House on the Prairie (1975), and played the uncredited violin solo on the title track of Pink Floyd's Wish You Were Here (1975), a contribution mixed nearly inaudible until the 2011 remaster restored it. Late in his life he recorded Flamingo (1996) with pianist Michel Petrucciani, bassist George Mraz and drummer Roy Haynes, one of his last major studio dates. In 1997 he received a Grammy Lifetime Achievement Award and was inducted into the Down Beat Jazz Hall of Fame.

Despite failing health, Grappelli continued touring into 1997, playing dates in the United Kingdom that March before a final tour of Australia and New Zealand; his last public performance was in Christchurch. He died in Paris on December 1, 1997, at eighty-nine, of heart failure following a series of minor strokes. His funeral was held December 5 at the Église Saint-Vincent-de-Paul, within sight of the hospital where he was born, and his ashes were entombed at the Père Lachaise Cemetery.

Grappelli belongs, with Joe Venuti and Stuff Smith, among the three musicians most responsible for establishing the violin as a genuine jazz solo instrument in the years before bebop. Where Venuti's attack could be hard-edged and combative, Grappelli's playing was sweeter and more legato, built on a singing tone, effortless swing and an unfailingly melodic sense of improvisation that he carried, essentially unchanged in its essentials, from the acoustic Quintette du Hot Club de France of the 1930s through five more decades of amplified small-group jazz. He remained remarkably consistent and enthusiastic to the end of his life, adapting to duo settings with a classical virtuoso (Yehudi Menuhin), a vibraphonist (Gary Burton), a bluegrass mandolinist (David Grisman) and fellow violinists (Jean-Luc Ponty, Svend Asmussen, Stuff Smith) without ever forcing his own vocabulary to fit theirs. Critics and younger violinists alike came to regard him as, in the phrase widely used by the end of his career, the grandfather of jazz violinists.