This paper considers the optimal constellation design for the generalized spatial modulation (GSM). The signal and spatial parts of the constellation are jointly designed where the signal part is not restricted to the conventional amplitude/phase modulation constellation points. The design problem is formulated as an optimization problem where a set of multi-dimensional constellation points that minimizes the average symbol error rate (SER) is selected. A gradient search algorithm is proposed to solve the optimization problem. Numerical results demonstrate the improved SER performance and increased energy efficiency of the proposed generalized signal- spatial constellation (GSSC) scheme as compared to previous spatial modulation (SM), GSM, and conventional MIMO schemes.