Campion was born in London and studied at Peterhouse, Cambridge before entering Gray's Inn to study law in 1586. However, it seems he never actually was a practicing lawyer. He later studied in Europe before returning to London and beginning to practice as a physician in 1606.
Campion was first published as a poet in 1591 with five of his works appearing in an edition of Sir Philip Sidney's Astrophel and Stella. The Songs for Mourning, published in 1613 after the death of Prince Henry, were set to music by John Cooper. He also wrote a number of other poems as well as a book on poetry, Observations in the Art of English Poesie (1602), in which he criticises the practice of rhyming in poetry.
Campion write over one hundred songs with lute accompaniment, with his first collection appearing in 1601 and four more following throughout the 1610s. He also wrote a number of masques. In 1615 he published a book on counterpoint, A New Way of Making Fowre Parts in Counterpoint By a Most Familiar and Infallible Rule, which was highly enough regarded to be reprinted in 1660.
Campion died in London, possibly of the plague.