During fast charging of Lithium-Ion batteries (LIB), cell overheating and overvoltage increase safety risks and lead to faster battery deterioration. Moreover, in conventional Battery Management Systems (BMS), the cell balancing, charging strategy and thermal regulation are treated separately at the expense of faster cell deterioration. Hence, this paper proposes an optimized fast charging and balancing strategy with electrothermal regulation of LIB packs. Thereby, the power dissipation constraints of the passive balancing are introduced in the proposed integrated optimal framework and cell balancing is achieved by bypassing the extra charging current. The electrothermal model of the cells, along with a battery pack formed by a string of cells, is implemented. Extensive experiments are carried out to identify the coefficients for the Lithium-Ion cell model, i.e. Samsung-INR18650-20R, and the charging current trajectory as well as the balancing signals are generated with Model Predictive Control (MPC). The pack level simulations and experiments show that the proposed algorithm maintains the electro-thermal boundaries throughout the charging process, increasing the safe charge acceptance of the battery pack.