The coexistence of electrical polarization and magnetization in multiferroic materials provides great opportunities for novel information storage systems. In particular, magnetoelectric (ME) effect can be realized in multiferroic composites consisting of both ferromagnetic and ferroelectric phases through a strain mediated interaction, which offers the possibility of electric field (E-field) manipulation of magnetic properties or vice versa, and enables novel multiferroic devices such as magnetoelectric random access memories (MERAMs). These MERAMs combine the advantages of FeRAMs (ferroelectric random access memories) and MRAMs (magnetic random access memories), which are non-volatile magnetic bits switchable by electric field (E-field). However, it has been challenging to realize 180 deterministic switching of magnetization by E-field, on which most magnetic memories are based. Here we show E-field modulating exchange bias and for the first time realization of near 180 dynamic magnetization switching at room temperature in novel AFM (antiferromagnetic)/FM (ferromagnetic)/FE (ferroelectric) multiferroic heterostructures of FeMn/Ni80Fe20/FeGaB/PZN-PT (lead zinc niobate-lead titanate). Through competition between the E-field induced uniaxial anisotropy and unidirectional anisotropy, large E-field-induced exchange bias field-shift up to Delta H-ex/H-ex = 218% and near 180 deterministic magnetization switching were demonstrated in the exchange-coupled multiferroic system of FeMn/Ni80Fe20/FeGaB/PZN-PT. This E-field tunable exchange bias and near 180 deterministic magnetization switching at room temperature in AFM/FM/FE multiferroic heterostructures paves a new way for MERAMs and other memory technologies.