Griesbach was educated at Frankfurt, and at the universities of Tübingen, Leipzig and Halle, where he became one of J. S. Semler's most ardent disciples.
On his return to Halle, Griesbach acted for some time as Privatdozent, but in 1773 was appointed to a professorial chair; in 1775 he went to the University of Jena, where he spent the rest of his life (though he received calls to other universities).