B737 First Officer reported the loss of both Engine Driven Hydraulic Pumps in flight. Faced with the possibility of a dual hydraulic system loss; the flight crew elected to divert and make a precautionary landing.

Narrative

Captain Name and I were operating Aircraft X; which was a second leg of ZZZ1-ZZZ turn. Upon arriving into ZZZ; on the Pilot App; we saw that there was going to be an aircraft swap. The aircraft which we were to operate was coming from a hangar. It apparently had HYD SYS A malfunction. Maintenance Personnel advised us that Engine Driven HYD PUMP for SYS A was replaced and maintenance release was cleared.During climb; Master Caution light end ENG HYD PUMP lights illuminated. QRH was accomplished. We contacted Dispatch and Maintenance Control. We were advised to monitor quantity and pressure for SYS A. Within the next ten minutes we observed HYD SYS A quantity drop to 20%. SYS A continued to operate normally on the electric pump.Captain and I referred to the FOM for systems review; and we also discussed at length any possible issue that may arise from this failure. The main issue of concern that the landing gear may not extend normally and manual gear extension maybe necessary. We conducted a system review and discussed our plan of action should SYS A completely fail. Upon starting our descent; LOW PRESSURE light for ENG Driven pump for engine #2 Illuminated. QRH was accomplished. Since we were faced with possibility of a dual HYD SYS loss; we made a decision to divert to ZZZ2. ATC was notified; priority handling was requested; and we were given vectors for ZZZ2. Once establish on final; we decided to lower the gear at approximately 10 mile final; to give us more time to address any issues should the gear fail to extend. Approach and landing were uneventful. We exited the runway and stopped on a high-speed taxiway. ARFF personnel observed fluid leaking from number one engine. At that point both engines were shut down; inspection by ARFF was completed; and we were pulled to the gate by a super tug.