Tilting theory in cluster categories of hereditary algebras has been developed in [BMRRT] and [BMR]. These results are generalized to cluster categories of hereditary abelian categories. Furthermore, for any tilting object T in a hereditary abelian category H, we verify that the tilting functor HomH(T,−) induces a triangle equivalence from the cluster category C(H) to the cluster category C(A),...