The son of the gymnasial headmaster Johann Philipp Crollius and Margaretha Gabriela Joannis, Crollius studied in Halle and Göttingen. He succeeded to his father in the management of the Herzog-Wolfgang-Gymnasium in Zweibrücken, the most renowned school in Palatinate-Zweibrücken. Duke Christian IV appointed him also to the committee of the library, the present-day Bibliotheca Bipontina, and to court historiographer. Similarly to his father he researched about the history of Palatinate-Zweibrücken and of the Rhenish County Palatine. As a member of the Mannheim academy (since 1765) he wrote several essays, which were printed in the series of the academy. The Origines Bipontinae (1761-1769) might be cited as his main work. Starting in 1779 he contributed also to the Editiones Bipontinae.