Mendelssohn was the son of a banker, Abraham, who was himself the son of the famous Jewish philosopher, Moses Mendelssohn, and of Lea Salomon, a member od the Itzig family. Abraham sought to renounce the Jewish religion; his children were first brought up without religious education, and were baptised as Lutherans in 1816. (Abraham and his wife were not themselves baptised until 1822). The name Bartholdy was assumed at the suggestion of Lea's brother, Jakob, who had purchased a property of this name and adopted it as his own surname. Abraham was later to explain this decision in a letter to Felix as a means of showing a decisive break with the traditions of his father Moses: 'There can no more be a Christian Mendelssohn than there can be a Jewish Confucius'. Although Felix continued to sign his letters as 'Mendelssohn Bartholdy' in obedience to his fsther's injunctions, he seems not to have objected to the use of 'Mendelssohn' alone.

The family moved to Berlin in 1812. His sister Fanny Mendelssohn (later Fanny Hensel), became a well-known pianist and amateur composer; originally Abraham had thought that she, rather than her brother, might be the more musical.

Mendelssohn is often considered the greatest child prodigy after Wolfgang Amadeus Mozart. He began taking piano lessons from his mother when he was six, and at seven was tutored by Marie Bigot in Paris. From 1817 he studied composition with Carl Friedrich Zelter in Berlin. He probably made his first public concert appearance at the age of nine, when he participated in a chamber music concert. He was also a prolific composer as a child, and wrote his first published work, a piano quartet, by the time he was thirteen. Zelter introduced Felix to his friend and correspondent, the elderly Goethe. Felix later took lessons from the composer and virtuoso Ignaz Moscheles who however confessed that he had little to teach him. Moscheles became a close colleague and lifelong friend.

As an adolescent, Felix's works were often performed at home with a private orchestra for the associates of his wealthy parents amongst the intellectual elite of Berlin. Mendelssohn wrote his first twelve symphonies in his early teens (more specifically, from ages twelve to fourteen). These works were ignored for over a century, but are now recorded and heard occasionally in concerts. At fifteen he wrote his first acknowledged symphony for full orchestra, his opus 11 in C minor in 1824. At the age of sixteen he wrote his String Octet in E Flat Major, the first work which showed the full power of his genius, and, together with his overture to Shakespeare's A Midsummer Night's Dream, which he wrote a year later, the best known of his early works. (He wrote incidental music for the play in 1842, including the famous Wedding March). In 1827 he saw the first production of his opera, Die Hochzeit des Camacho.

In 1829 Mendelssohn paid his first visit to England, where Moscheles, already settled in London, introduced him to influential musical circles. Felix had a great success, conducting his First Symphony and playing in public and private concerts. On subsequent visits he met with Queen Victoria and her musical husband Prince Albert, both of whom were great admirers of his music. In the course of ten visits to Britain during his life he won a strong following, and the country inspired two of his most famous works, the overture Fingal's Cave (also known as the Hebrides Overture) and the Scottish Symphony (Symphony no.3). His oratorio Elijah was premiered in Birmingham on August 26, 1846.

In 1835, he was appointed as conductor of the Gewandhausorchester Leipzig. This appointment was extremly important for him as he felt himself to be a German and wished to play a leading part in his country's musical life. Despite efforts by the king of Prussia to lure him to Berlin, Mendelssohn sought to develop the musical life of Leipzig and in 1843 he founded the Leipzig Conservatory, where he succesfully persuaded Moscheles to join him.

Mendelssohn's personal life was conventional. His marriage to Cecile Jeanrenaud in March of 1837 was very happy and the couple had five children. Felix was an accomplished painter in water-colour, and his enormous correspondence shows that he could also be a witty writer (in both German and English - and sometimes accompanied by humorous sketches and cartoons in the text).

Mendelssohn suffered from bad health in the final years of his life, probably aggravated by nervous problems and overwork, and he was greatly distressed by the death of his sister Fanny in May 1847. Felix Mendelssohn died later that same year after a series of strokes, in Leipzig. He is buried in the Dreifaltigkeitsfriedhof (Trinity Cemetery) I in Berlin-Kreuzberg.