We study the theoretical foundations of the recently developed large-momentum effective theory (LaMET) approach to the transverse-momentum-dependent parton distribution function (TMDPDF). We first show that the quasi-TMDPDF can be consistently defined and it relates to the physical TMDPDFs through a factorization formula in the large-momentum limit. We show that the factorization involves the intrinsic soft function which is related to the off-lightcone soft functions for the Drell–Yan process and can be realized as a form factor. We also study properties of the off-lightcone soft functions, such as IR safety, analyticity, rapidity divergence, etc. Universality classes of the off-lightcone soft functions are discussed. Finally, we show that the intrinsic soft function can be extracted by combining a light-meson form factor with large-momentum transfer and quasi-TMD wave functions for the light meson.