Christoph Klau was born in Bamberg in 1538. We know little about his childhood and early youth, and it is not even certain whether his surname was Klau or Schlüsse, only that it was Latinized into Clavius. In 1555, at the age of seventeen, Clavius joined the Jesuit Order in Rome and the following year was sent to Coimbra to complete his university studies, showing a particular aptitude for mathematics. In 1560 he returned to Rome, where he soon became a professor at the Roman College. Clavius wrote many works on mathematics and astronomy, which gained him an increasingly authoritative reputation. The most celebrated were his edition of Euclid's (4th century B.C.) Elements and a commentary on Giovanni di Sacrobosco's (c.1190-c.1250) De sphaera. Clavius also took part in the committee that reformed the calendar under Pope Gregory XIII and went into effect in 1582. He was so highly esteemed that his contemporaries nicknamed him the "Euclid of our time".

In his books on astronomy Clavius opposed the Copernican system on both physical and theological grounds, a position he maintained even after Galileo's discoveries.

Galileo formed close ties with Clavius from their university days, having met him during his first trip to Rome in 1587, and kept up a steady correspondence with him, offering his help on mathematical questions. Clavius, though at first sceptical, was determined to dispel any doubts about the celestial observations in Sidereus nuncius [Starry Messenger], announcing in 1610 that he had definitely seen Jupiter's moons and congratulating Galileo on his discovery.

In April of 1611 Cardinal Roberto Bellarmino (1642-1621) asked Clavius and his group of astronomers to formulate a critique of Galileo's new astronomical revelations. The group expressed a substantially positive opinion in confirmation of Galileo's observations. Clavius, in the latest edition of Sacrobosco's De Sphaera published in 1611 in the third volume of his Opera mathematica, called for a re-examination of the composition of the celestial bodies so as to "save the phenomena", a declaration interpreted by some as a last-minute conversion to Copernicanism on Clavius' part, while more likely he was merely aiming to readjust the Ptolemaic system in order to account for these new phenomena.

Clavius died in February of 1612.