Stravinsky was born on 17 June 1882 in Oranienbaum, a suburb of Saint Petersburg, the Russian imperial capital, and was brought up in Saint Petersburg.

Despite his enthusiasm for music and their musical background, his parents expected him to study law. Stravinsky enrolled at the University of Saint Petersburg in 1901, but he attended fewer than fifty class sessions during his four years of study.

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.

After getting his half-course diploma, he concentrated on studying music. 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, Stravinsky was engaged to his cousin Katherine Gavrylivna Nosenko (called "Katya"), whom he had known since early childhood. In spite of the Orthodox Church's opposition to marriage between first cousins, the couple married on 23 January 1906.

The university was closed for two months in 1905 in the aftermath of Bloody Sunday, Stravinsky was prevented from taking his final law examinations and later received a half-course diploma in April 1906.

In 1907, Stravinsky designed and built his own house in Ustilug, which he called "my heavenly place". In this house, Stravinsky worked on seventeen of his early compositions, among them Feu d'artifice, The Firebird, Petrushka, and The Rite of Spring. Recently renovated, the house is now a Stravinsky house-museum open to the public.

In February 1909, two of Stravinsky's orchestral works, the Scherzo fantastique and Feu d'artifice (Fireworks) were performed at a concert in Saint Petersburg, where they were heard by Serge 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 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. After spending the summer in La Baule, Brittany, they moved to Switzerland in early September.

On 23 September, their second son, Sviatoslav Soulima, was born at a maternity clinic in Lausanne; at the end of the month, they took up residence in Clarens.

Shortly following the premiere of The Rite of Spring on 29 May 1913, Stravinsky contracted typhoid from eating bad oysters, and was confined to a Paris nursing home, unable to depart for Ustilug until 11 July.

The Stravinsky family returned to Switzerland (as usual) in the fall of 1913. On 15 January 1914, a fourth child, Marie Milène (or Maria Milena), was born in Lausanne. After her delivery, Katya was discovered to have tuberculosis and was confined to the sanatorium at Leysin, high in the Alps. Igor and the family took up residence nearby.

Stravinsky turned his attention to completing his first opera, the Nightingale (usually known by its French title Le Rossignol), which he had begun in 1908 (that is, before his association with the Ballets Russes). The work had been commissioned by the Moscow Free Theatre for the handsome fee of 10,000 rubles. and he completed Le Rossignol at Leysin on 28 March, 1914.

In April, they were finally able to return to Clarens.

As the Moscow Free Theatre had gone bankrupt, 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.

In July 1914, with war looming, Stravinsky made a quick trip to Ustilug to retrieve personal effects including his reference works on Russian folk music. He returned to Switzerland just before national borders closed following the outbreak of World War I. 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.

In April 1915, Stravinsky received a commission from Winnaretta Singer (Princesse Edmond de Polignac) for a small-scale theatrical work to be performed in her Paris salon. The result was Renard (1916), which he called "A burlesque in song and dance".

In June 1915, Stravinsky and his family moved from Clarens to Morges, a town six miles south-west of Lausanne on the shore of Lake Geneva. The family lived there (at three different addresses) until 1920.

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. Stravinsky blamed Diaghilev for his financial troubles, accusing him of failing to live up to the terms of a contract they had signed. He approached the Swiss philanthropist Werner Reinhart for financial assistance while he was writing L'Histoire du soldat (The Soldier's Tale). Reinhart sponsored and largely underwrote its 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.

On 8 June 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 The Rite of Spring with an anonymous gift to Diaghilev, said to have been 300,000 francs.

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, southwestern France.

In September 1924, Stravinsky bought "an expensive house" in Nice: the Villa des Roses.

From 1931 to 1933, the Stravinskys lived in Voreppe, near Grenoble, southeastern France.

The Stravinskys became French citizens in 1934 and moved to the rue du Faubourg Saint-Honoré in Paris.

From their moving to Anglet until his wife's death in 1939, Stravinsky led a double life, dividing his time between his family in Anglet, and Vera in Paris and on tour. Katya reportedly bore her husband's infidelity "with a mixture of magnanimity, bitterness, and compassion".

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 and thence to Cambridge, Massachusetts, to fulfill his engagement at Harvard.

Vera followed Stravinsky in January, and they were married in Bedford, Massachusetts, on 9 March 1940.

Stravinsky's unconventional dominant seventh chord in his arrangement of the "Star-Spangled Banner" led to an incident with the Boston police on 15 January 1944, and he was warned that the authorities could impose a $100 fine upon any "re-arrangement of the national anthem in whole or in part". The police, as it turned out, were wrong. The law in question merely forbade using the national anthem "as dance music, as an exit march, or as a part of a medley of any kind", but the incident soon established itself as a myth, in which Stravinsky was supposedly arrested, held in custody for several nights, and photographed for police records.

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.

In 1951, he completed his last neoclassical work, the opera The Rake's Progress to a libretto by W.H. Auden and Chester Kallman based on the etchings of William Hogarth. It premiered in Venice that year and was produced around Europe the following year before being staged in the New York Metropolitan Opera in 1953.

In 1959, he was awarded the Sonning Award, Denmark's highest musical honour.

In September 1962, Stravinsky returned to Russia for the first time since 1914, accepting an invitation from the Union of Soviet Composers to conduct six performances in Moscow and Leningrad. During the three-week visit he met with Soviet Premier Nikita Khrushchev and several leading Soviet composers, including Dmitri Shostakovich and Aram Khachaturian.

In October 1969, Stravinsky relocated to an apartment in Essex House in New York City. Among Stravinsky's final projects was orchestrating two preludes from The Well-Tempered Clavier by Bach, but it was never completed.

On 18 March 1971, Stravinsky was taken to Lenox Hill Hospital with pulmonary edema where he stayed for ten days.

On 29 March, he moved into a newly furbished apartment at 920 Fifth Avenue, his first city apartment since living in Paris in 1939.

After a period of well being, the edema returned on 4 April and Vera insisted that medical equipment should be installed in the apartment.

Stravinsky stopped eating and drinking and died at 5:20 a.m. on 6 April at the age of 88. The cause on his death certificate is heart failure. A funeral service was held three days later at Frank E. Campbell Funeral Chapel. As per his wishes, he was buried in the Russian corner of the cemetery island of San Michele in northern Italy, several yards from the tomb of Sergei Diaghilev.