Let A be a finite dimensional algebra over an algebraically closed field K. The derived Picard group DPic_k(A) is the group of two-sided tilting complexes over A modulo isomorphism. We prove that DPic_k (A) is a locally algebraic group, and its identity component is Out(A). If B is a derived Morita equivalent algebra then DPic_K(A)≅DPic_K(B) as locally algebraic groups.