Campion was born in London, the son of John Campion, a clerk of the Court of Chancery, and Lucy (née Searle – daughter of Laurence Searle, one of the queen's serjeants-at-arms). Upon the death of Campion's father in 1576, his mother married Augustine Steward, dying soon afterwards. His stepfather assumed charge of the boy and sent him, in 1581, to study at Peterhouse, Cambridge as a "gentleman pensioner"; he left the university after four years without taking a degree. He later entered Gray's Inn to study law in 1586. However, he left in 1595 without having been called to the bar.
On 10 February 1605, he received his medical degree from the University of Caen.
Campion is thought to have lived in London, practising as a physician, until his death in March 1620 – possibly of the plague. He was apparently unmarried and had no children. He was buried the same day at St Dunstan-in-the-West in Fleet Street.
He was implicated in the murder of Sir Thomas Overbury, but was eventually exonerated, as it was found that he had unwittingly delivered the bribe that had procured Overbury's death.