He was born in Neuhausen, and was educated in Heidelberg. The Protestant Cellarius may have left Heidelberg at the onset of the Thirty Years' War in 1618 or in 1622, when the city came in Catholic hands. His activities are unclear at this time but based on his later works it is conjectured that he spent time in Poland where he may have worked as a military engineer.
In 1625, he married Catharina Eltemans in Amsterdam, where he worked as school master of a Latin school. After a brief stay in The Hague, the family moved to Hoorn. From 1637 until his death, he was rector of the Latin School in Hoorn, where Pieter Anthoniszoon Overtwater was conrector.
The minor planet 12618 Cellarius is named in his honour.