Silicon photonics is emerging as a competitive platform for electronic-photonic integrated circuits (EPICs) at the 2 µm wavelength band where GeSn photodetectors (PDs) have proven to be efficient PDs. Here, we present a comprehensive theoretical study of GeSn vertical p-i-n homojunction waveguide photodetectors (WGPDs) that have a strain-free and defect-free GeSn active layer for 2-µm Si-based EPICs. The use of a narrow-gap GeSn alloy as the active layer can fully cover entire the 2 µm wavelength band. The waveguide structure allows for decoupling the photon-absorbing path and the carrier-collection path, thereby allowing for simultaneous achievement of high-responsivity and high-bandwidth (BW) operation at the 2-µm wavelength band. We present the theoretical models to calculate the carrier saturation velocities, optical absorption coefficient, responsivity, 3-dB bandwidth, zero-bias resistance, and detectivity, and optimize this device structure to achieve highest performance at the 2-µm wavelength band. The results indicate that the performance of the GeSn WGPD has strong dependence on the Sn composition and geometric parameters. The optimally designed GeSn WGPD with 10% Sn concentration can give responsivity of 1.55 A/W, detectivity of 6.12×1010 cmHz½W-1 at 2 µm wavelength, and ~97 GHz BW. Therefore, this optimally designed GeSn WGPD is a potential candidate for silicon photonic EPICs offering high-speed optical communications.