In this paper, we show how the phenomenon of inertia can be explained in non-relativistic classical mechanics using a unified theory of gravity and inertia. As a basis, we used the inertia-free mechanics of H.J. Treder. It can implement both Mach’s principle and the idea of inertia having a gravitational origin without the shortcomings of an anisotropic inertial mass. Inertia arises from a velocity-dependent part of the gravitational potential. Thus, it will be possible to formulate classical mechanics with postulating neither the weak equivalence principle, nor a gravitational constant, nor any concept of inertial mass or inertial forces a priori. We will show that all four can be derived from the theory. The theory is valid in arbitrary accelerated frames of reference and the inertial frames are determined by all other particles in the universe, as demanded by Mach’s principle. The exact Newtonian inertial forces will appear in any non-inertial frame, for translational and rotational acceleration, showing that they are not fictitious, but real parts of the gravitational force. In the lowest order v/c of the theory, Newtonian mechanics is obtained. The corrections that appear are shown to be just the terms present in Gravitoelectromagnetism. Ultimately, explaining inertia as a gravitational effect will allow us to derive an expression for the gravitational constant, enabling us to explain the apparent weakness of gravity. Such a unified theory of gravity and inertia has profound implications for the nature of mass and structure of elementary particles, as well as the origin of relativistic and quantum effects. This suggests a very different path towards a combined theory of relativity, gravity, and quantum mechanics, as well as elementary particles. This will be discussed in a subsequent paper.