We demonstrate a voltage-controlled exchange bias effect in CoFeB/MgO/CoFeB magnetic tunnel junctions that is related to the interfacial Fe(Co)O_{x} formed between the CoFeB electrodes and the MgO barrier. The unique combination of interfacial antiferromagnetism, giant tunneling magnetoresistance, and sharp switching of the perpendicularly magnetized CoFeB allows sensitive detection of the exchange bias. We find that the exchange bias field can be isothermally controlled by magnetic fields at low temperatures. More importantly, the exchange bias can also be effectively manipulated by the electric field applied to the MgO barrier due to the voltage-controlled antiferromagnetic anisotropy in this system.