This paper deals with the construction of explicit compact supersymmetric valid solutions with non-zero field strength, non-flat instantons and constant dilaton to the heterotic string equations in dimensions 7 and 8. It is worth to mention that the non-compact solutions in dimensions 7 and 8 are already provided in [P. Ivanov and S. Ivanov, Commun. Math. Phys. 259, No. 1, 79–102 (2005; Zbl 1082.53027)]. In this paper, the authors present compact nilmanifolds in dimensions 7 and 8 which are supersymmetric solutions of the heterotic string equations in dimensions 7 and 8. The construction of the solutions in dimension 7 are based on the seven-dimensional generalized Heisenberg nilmanifold and in dimension 8 can be described as a circle bundle over a six-torus with curvature inside the Lie algebra \(\mathrm{su}(3)\) or as the total space of a circle bundle with curvature inside a Lie algebra (a compact, connected, simply connected, simple subgroup of \(\mathrm{SO}(7)\) of dimension 14) over a seven-manifold which is a circle bundle over a six-torus. Moreover, the authors demonstrate that some of their examples are compact supersymmetric solutions of heterotic string equations in dimensions 7 and 8.