The concept of cotorsion was first introduced in the category of Abelian groups (Fuchs [l] ). Matlis [5], studied the cotorsion modules over integral domains. Henderson and Orzech [4], Fuchs [2], and Mines [6], replaced the classical notion of torsion by a torsion theory (T,F) on R-mod, where R is not necessarily commutative ring. In this paper we find conditions on the torsion theory in order to get a T-cotorsion hull for every module. This generalizes the result of Fuchs [2].