A hydraulic excavator drive system includes: a first hydraulic pump and a second hydraulic pump, whose respective tilting angles are controllable independently of each other; an arm main control valve and an arm auxiliary control valve each for controlling supply of hydraulic oil to an arm cylinder; and a boom main control valve and a boom auxiliary control valve each for controlling supply of the hydraulic oil to a boom cylinder. An arm operation valve outputs a pilot pressure to the arm main control valve. A boom operation valve outputs a pilot pressure to the boom main control valve. A pair of arm-side regulating valves outputs no pilot pressure to the arm auxiliary control valve and a boom-side regulating valve outputs no pilot pressure to the boom auxiliary control valve when an arm crowding operation and a boom raising operation are performed concurrently.