In this Letter, we show how to efficiently generate entanglement between two artificial giant atoms with photon-mediated interactions in a waveguide. Taking advantage of the adjustable decay processes of giant atoms into the waveguide and of the interference processes, spontaneous sudden birth of entanglement can be strongly enhanced with giant atoms. Highly entangled states can also be generated in the steady-state regime when the system is driven by a resonant classical field. We show that the statistics of the light emitted by the system can be used as a witness of the presence of entanglement in the system, since giant photon bunching is observed close to the regime of maximal entanglement. Given the degree of quantum correlations incoherently generated in this system, our results open a broad avenue for the generation of quantum correlations and manipulation of photon statistics in systems of giant atoms.