A three-dimensional transient model for time-domain (modulated) free-carrier absorption (FCA) measurement was developed to describe the transport dynamics of photo-generated excess carriers in silicon (Si) wafers. With the developed transient model, numerical simulations were performed to investigate the dependences of the waveforms of the transient FCA signals on the electronic transport parameters of Si wafers and the geometric parameters of the FCA experiment. Experimental waveforms of FCA signals of both n- and p-type Si wafers with resistivity ranging 1–38 Ω·cm were then fitted to the three-dimensional transient model to extract simultaneously and unambiguously the transport parameters of Si wafers, namely, the carrier lifetime, the carrier diffusion coefficient, and the front surface recombination velocity via multi-parameter fitting. A basic agreement between the extracted parameter values and the literature values was obtained.