Ever since the first observation of all-optical switching of magnetization in the ferrimagnetic alloy GdFeCo using femtosecond laser pulses, there has been significant interest in exploiting this process for data-recording applications. In particular, the ultrafast speed of the magnetic reversal can enable the writing speeds associated with magnetic memory devices to be potentially pushed towards THz frequencies. This work reports the development of perpendicular magnetic tunnel junctions incorporating a stack of Tb/Co nanolayers whose magnetization can be all-optically controlled via helicity-independent single-shot switching. Toggling of the magnetization of the Tb/Co electrode was achieved using either 60 femtosecond-long or 5 picosecond-long laser pulses, with incident fluences down to 3.5 mJ/cm , for Co-rich compositions of the stack either in isolation or coupled to a CoFeB-electrode/MgO-barrier tunnel-junction stack. Successful switching of the CoFeB-Tb/Co electrodes was obtained even after annealing at 250  C. After integration of the Tb/Co-based electrodes within perpendicular magnetic tunnel junctions yielded a maximum tunneling magnetoresistance signal of 41% and RxA value of 150 Ωμm with current-in-plane measurements and ratios between 28% and 38% in nanopatterned pillars. These results represent a breakthrough for the development of perpendicular magnetic tunnel junctions controllable using single laser pulses, and offer a technologically-viable path towards the realization of hybrid spintronic-photonic systems featuring THz switching speeds.