There are several classes of operators defined and studied on the Hardy space of which shift operators are an important class. In 1949, Beurling characterized the invariant subspaces of the unilateral shift operator. A natural generalization of scalar weighted shift is the operator weighted shift which is our object of study. We define operator weighted shifts on Hardy Spaces over a separable complex Hilbert space. Following this the spectrum, the invariant subspaces and the (minimal) reducing subspaces of these operators are determined and analyzed. A discussion on hypercyclic...