  We construct a black-hole spacetime which includes the running of the
gravitational coupling in a self-consistent way. Starting from a classical
Schwarzschild black hole, the backreaction effects produced by the running
Newton's coupling are taken into account iteratively. The sequence, described
by a simple recurrence relation, flows towards a self-consistent solution that
can be derived analytically. As a key result, if the gravitational
renormalization group flow attains a non-trivial fixed point at high energies,
the sequence converges to a "renormalized" black-hole spacetime of the
Dymnikova-type, which is free of singularities.
