We determine the number of Del Pezzo surfaces of degree 2 over finite fields of odd characteristic with specified action of the Frobenius endomorphism, i.e., we solve the “quantitative inverse Galois problem”. As applications we determine the number of Del Pezzo surfaces of degree 2 with a given number of points and recover results of Banwait, Fité and Loughran and Loughran and Trepalin.