In this paper, we present a closed-form solution to the problem of optimally charging a Li-ion battery. The objective function is considered as a combination of two cost functions: time-to-charge (TTC) and energy losses (EL). For the case where cost function is a combination of TTC and EL, the optimal charging strategy is a Constant Current-Constant Voltage (CC-CV) policy with the value of the current in the CC stage being a function of the ratio of weighting on TTC and EL and of the resistance of the battery. The case where the cost function is a weighted sum of TTC, EL and a temperature rise index (TRI) is also considered and an analytical solution for the problem is derived. This analytical solution can be approximated by a CC-CV with the value of current in the CC stage being a function of ratio of weighting on TTC and EL, resistance of the battery and the effective thermal resistance. The effects of weights in the objective function on the optimal charging profile is discussed and the behavior of different kinds of commercial batteries are analyzed.