We consider the problem of maximizing the harvested power in Multiple Input Multiple Output (MIMO) Simultaneous Wireless Information and Power Transfer (SWIPT) systems with power splitting reception. Different from recently proposed designs, we target with our novel problem formulation at the jointly optimal transmit precoding and receive uniform power splitting (UPS) ratio maximizing the harvested power, while ensuring that the Quality-of-Service (QoS) requirement of the MIMO link is satisfied. We assume generic practical Radio Frequency (RF) Energy Harvesting (EH) receive operation that results in a non-convex optimization problem for the design parameters, which we then solve optimally after formulating it in an equivalent generalized convex form. Our representative results including comparisons of achievable EH gains with benchmark schemes provide key insights on various system parameters.