Stravinsky was born in Oranienbaum (modern Lomonósov), a suburb of Saint Petersburg, the Russian imperial capital, and was brought up in Saint Petersburg. His parents were Fyodor Stravinsky, a bass singer at the Mariinsky Theatre in St. Petersburg, and Anna (née Kholodovsky). Stravinsky began piano lessons as a young boy, studying music theory and attempting composition. Despite his enthusiasm for music, his parents expected him to study law. Stravinsky enrolled at the University of Saint Petersburg in 1901. In the summer of 1902 Stravinsky stayed with composer Nikolai Rimsky-Korsakov and his family in the German city of Heidelberg, where Rimsky-Korsakov, arguably the leading Russian composer at that time, suggested to Stravinsky that he should not enter the Saint Petersburg Conservatoire, but instead study composing by taking private lessons, in large part because of his age. In 1905, he began to take twice-weekly private lessons from Rimsky-Korsakov, whom he came to regard as a second father.These lessons continued until Rimsky-Korsakov's death in 1908.

In 1905 he was betrothed to his cousin Yekaterina Gavrilovna Nosenko (called "Katya"), whom he had known since early childhood. The couple married on 23 January 1906: their first two children, Fyodor (Theodore) and Ludmila, were born in 1907 and 1908, respectively.

In February 1909, two orchestral works, the Scherzo fantastique and Feu d'artifice (Fireworks) were performed at a concert in Saint Petersburg, where they were heard by Sergei Diaghilev, who was at that time involved in planning to present Russian opera and ballet in Paris. Diaghilev was sufficiently impressed by Fireworks to commission Stravinsky to carry out some orchestrations and then to compose a full-length ballet score, The Firebird.

Stravinsky became an overnight sensation following the success of The Firebird's premiere in Paris on 25 June 1910.

The composer had travelled from his estate in Ustilug, Ukraine, to Paris in early June to attend the final rehearsals and the premiere of The Firebird. His family joined him before the end of the ballet season and they decided to remain in the West for a time, as his wife was expecting their third child. They moved to Switzerland in early September. Over the next four years, Stravinsky and his family lived in Russia during the summer months and spent each winter in Switzerland. During this period, Stravinsky composed two further works for the Ballets Russes: Petrushka (1911), and Le Sacre du printemps (The Rite of Spring; 1913).

During the remainder of the summer, Stravinsky turned his attention to completing his first opera, Le Rossignol, which he had begun in 1908 (that is, before his association with the Ballets Russes). The Stravinsky family returned to Switzerland (as usual) in the fall of 1913. Le Rossignol was first performed under Diaghilev's auspices at the Paris Opéra on 26 May 1914, with sets and costumes designed by Alexandre Benois. Le Rossignol enjoyed only lukewarm success with the public and the critics, apparently because its delicacy did not meet their expectations of the composer of The Rite of Spring. However, composers including Maurice Ravel, Béla Bartók, and Reynaldo Hahn found much to admire in the score's craftsmanship, even alleging to detect the influence of Arnold Schoenberg.

The War and subsequent Russian Revolution made it impossible for Stravinsky to return to his homeland, and he did not set foot upon Russian soil again until October 1962.

Stravinsky struggled financially during this period. Russia (and its successor, the USSR) did not adhere to the Berne convention and this created problems for Stravinsky when collecting royalties for the performances of all his Ballets Russes compositions.

The Swiss philanthropist Werner Reinhart sponsored Histoire du soldat’s first performance, conducted by Ernest Ansermet on 28 September 1918 at the Théâtre Municipal de Lausanne. In gratitude, Stravinsky dedicated the work to Reinhart and gave him the original manuscript.

Following the premiere of Pulcinella by the Ballets Russes in Paris on 15 May 1920, the entire family left Morges for the last time, and moved to the fishing village of Carantec in Brittany for the summer while also seeking a new home in Paris. On hearing of their dilemma, couturière Coco Chanel invited Stravinsky and his family to reside at her new mansion "Bel Respiro" in the Paris suburb of Garches until they could find a more suitable residence; they arrived during the second week of September. At the same time, Chanel also guaranteed the new (December 1920) Ballets Russes production of Stravinsky's Le Sacre du Printemps (The Rite of Spring).

Stravinsky met Vera de Bosset in Paris in February 1921, while she was married to the painter and stage designer Serge Sudeikin, and they began an affair that led to Vera leaving her husband. In May 1921, Stravinsky and his family moved to Anglet, near Biarritz, in the south of France. From then until his wife's death in 1939, Stravinsky led a double life, dividing his time between his family in southern France, and Vera in Paris and on tour.

His wife's tuberculosis infected both himself and his eldest daughter Ludmila, who died in 1938. Katya, to whom he had been married for 33 years, died of tuberculosis a year later, in March 1939. Stravinsky himself spent five months in hospital, during which time his mother died.

Despite the outbreak of World War II on 1 September 1939, the widowed Stravinsky sailed (alone) for the United States at the end of the month, arriving in New York City. Vera followed him in January, and they were married in Bedford, Massachusetts, on 9 March 1940.

Stravinsky settled in West Hollywood. He spent more time living in Los Angeles than any other city. He became a naturalized United States citizen in 1945.

Stravinsky had adapted to life in France, but moving to America at the age of 57 was a very different prospect. For a while, he maintained a circle of contacts and emigré friends from Russia, but he eventually found that this did not sustain his intellectual and professional life. He was drawn to the growing cultural life of Los Angeles, especially during World War II, when so many writers, musicians, composers and conductors settled in the area: these included Otto Klemperer, Thomas Mann, Franz Werfel, George Balanchine and Arthur Rubinstein. Bernard Holland claimed Stravinsky was especially fond of British writers, who visited him in Beverly Hills, like Auden, with whom he wrote The Rake’s Progress.

Stravinsky's professional life encompassed most of the 20th century, including many of its modern classical music styles, and he influenced composers both during and after his lifetime. In 1959, he was awarded the Sonning Award, Denmark's highest musical honour. In 1962, he accepted an invitation to return to Leningrad for a series of concerts. During his stay in the USSR, he visited Moscow and met several leading Soviet composers, including Dmitri Shostakovich and Aram Khachaturian.

In 1969, Stravinsky moved to the Essex House in New York, where he lived until his death in 1971 at age 88 of heart failure. He was buried at San Michele, close to the tomb of Diaghilev.

He has a star on the Hollywood Walk of Fame and in 1987 he was posthumously awarded the Grammy Award for Lifetime Achievement. He was posthumously inducted into the National Museum of Dance's Mr. & Mrs. Cornelius Vanderbilt Whitney Hall of Fame in 2004.