Ever since its discovery around a decade ago, all-optical magnetization switching (AOS) using femtosecond laser pulses has shown potential for future data storage and logic devices. In particular, single pulse helicity independent AOS in certain ferrimagnetic alloys and multilayers is highly efficient and ultrafast. However, in most cases it is a toggle mechanism, which is not desirable for applications. Here we experimentally demonstrate conversion from toggle switching to a deterministic mechanism by biasing AOS in a Co/Gd bilayer with a spin polarized current which is optically generated in an adjacent ferromagnetic reference layer. We show deterministic writing of an 'up' and 'down' state using a sequence of one or two pulses, respectively, and demonstrate the non-local origin by varying the magnitude of the generated spin current. Our demonstration of deterministic magnetization writing could provide an essential step towards the implementation of future optically addressable spintronic memory devices.