  We present an exact static black hole solution of Einstein field equations in
the framework of Horndeski Theory by imposing spherical symmetry and choosing
the coupling constants in the Lagrangian so that the only singularity in the
solution is at $r=0$. The analytical extension is built in two particular
domains of the parametric space. In the first domain we obtain a solution
exhibiting an event horizon analogous to that of the Schwarzschild geometry.
For the second domain, we show that the metric displays an exterior event
horizon and a Cauchy horizon which encloses a singularity. For both branches we
obtain the corresponding Hawking temperature which, when compared to that of
the Schwarzschild black hole, acquires a correction proportional to a
combination of the coupling constants. Such a correction also modifies the
definition of the entropy of the black hole.
