In this article, we prove the existence of the polar decomposition of densely defined closed right linear operators in quaternionic Hilbert spaces: If T is a densely defined closed right linear operator in a quaternionic Hilbert space H, then there exists a partial isometry U0 such that T=U0T. In fact U0 is unique if N(U0) = N(T). In particular, if H is separable and U is a partial isometry with T=U|T|, then we prove that U = U0 if and only if either N(T) = (0) or R(T)⊥ = (0). © 2016 AIP Publishing LLC.