Bouterwek studied law and philology under Christian Gottlob Heyne and Johann Georg Heinrich Feder at the University of Göttingen.
After he had finished his studies he was appointed to the Hanover Appellate Court, whilst, backed by Johann Wilhelm Ludwig Gleim, he also gave his debut as an author under the pen name Ferdinand Adrianow in the Göttinger Musenalmanach published by Gottfried August Bürger. He returned to Göttingen as a lecturer in history, from 1790, however, he became a disciple of Immanuel Kant and published Aphorismen nach Kants Lehre vorgelegt (1793). In 1802 he became professor ordinarius of philosophy at Göttingen, where he remained till his death.
As a philosopher, he is interesting for his criticism of the theory of the "thing-in-itself" (Ding-an-sich, noumenon). For the pure reason, as described in the Kritik, the "thing-in-itself" can be only an inconceivable "something-in-general"; any statement about it involves the predication of Reality, Unity and Plurality, which belong not to the absolute thing but to phenomena. On the other hand, the subject is known by the fact of will, and the object by that of resistance; the cognizance of willing is the assertion of absolute reality in the domain of relative knowledge. This doctrine has since been described as absolute Virtualism.
Following this train of thought, Bouterwek left the Kantian position through his opposition to its formalism. In later life he inclined to the views of Friedrich Heinrich Jacobi, whose letters to him (published at Göttingen, 1868) shed much light on the development of his thought.
Bouterwek died at Göttingen, Kingdom of Saxony.