A hydraulic excavator drive system includes: a boom cylinder; a boom first control valve connected to the boom cylinder by a boom raising supply line and a boom lowering supply line, and connected to a first pump by a first boom distribution line; a boom second control valve connected to the boom raising supply line by a boom replenishment line, and connected to a second pump by a second boom distribution line; an arm cylinder; an arm control valve connected to the arm cylinder by an arm crowding supply line and an arm pushing supply line, and connected to the second pump by an arm distribution line; a regenerative line connecting between the boom replenishment line and the arm distribution line; and an openable and closeable regenerative valve provided on the regenerative line.