A hydraulic excavator drive system includes: a first pump connected to a head-side chamber of a boom cylinder; and a second pump that supplies hydraulic oil to at least one of an arm cylinder or a bucket cylinder. The first pump is driven by an electric motor. The drive system further includes: a first switching valve located on a rod-side line; and a second switching valve located on a relay line. The first switching valve opens the rod-side line at a boom raising operation, but blocks the rod-side line except at the boom raising operation. The second switching valve blocks the relay line at the boom raising operation, but opens the relay line at a vehicle body lifting operation.