We have demonstrated the integrated indium gallium arsenide/indium aluminum arsenide (InGaAs/InAlAs) single-photon avalanche diodes (SPAD) with silicon (Si) waveguides and grating couplers on the Silicon-on-insulator substrate. A vertical coupling scheme is adopted which allows the use of a thick bonding interlayer for high yield. The epoxy ‘SU-8’ is selected to be the adhesion layer with a low transmission loss, low volumetric shrinkage, and low curing temperature. In addition, both hybrid and heterogeneous integration schemes are realized which are compatible with the current multi-project wafer process. Extensive performance characterization is carried out while the results are compared. Our hybrid integrated SPAD exhibits high photon detection efficiency (PDE) of ∼21% and a relatively low dark count rate (DCR) of 8.6 × 105 Hz, which are among the best performance reported for InGaAs/InAlAs SPADs while the heterogeneous integrated SPAD shows a decent PDE of 6% with a DCR of 2 × 107 Hz. Combined with the inherent wide applicability of the bonding using the SU-8 layer, this photonic integration provides a promising solution for large-scale quantum information with various material systems.