  Certain classical field theories admit a formal multi-particle solution,
known as the perturbiner expansion, that serves as a generating function for
all the tree-level scattering amplitudes and the Berends-Giele recursion
relations they satisfy. In this paper it is argued that the minimal model for
the $L_{\infty}$-algebra that governs a classical field theory contains enough
information to determine the perturbiner expansion associated to such theory.
This gives a prescription for computing the tree-level scattering amplitudes by
inserting the perturbiner solution into the homotopy Maurer-Cartan action for
the $L_{\infty}$-algebra. We confirm the method in the non-trivial examples of
bi-adjoint scalar and Yang-Mills theories.
