Owing to the tunable bandgap and high thermodynamic stability, anisotropic monolayer (ML) GeAs have arisen as an attractive candidate for electronic and optoelectronic applications. The contact properties of ML GeAs with 2D metal (graphene, Ti2CF2, V2CF2, and Ti3C2O2) and Cu electrodes are explored along two principal axes in field-effect transistors (FET) by employing ab initio electronic structure calculations and quantum transport simulations. Weak van der Waals interactions are found between ML GeAs and the 2D metal electrodes with the band structure of ML GeAs kept the same, while there is a strong interaction between ML GeAs and the Cu metal electrode, resulting in the obvious hybridization of the band structure. Isotropic contact properties are seen along the two principal directions. P-type lateral Schottky contacts are established in ML GeAs FETs with Ti3C2O2, graphene, and Ti2CF2 metals, with a hole Schottky barrier height (SBH) of 0.12 (0.20), 0.15 (0.11), and 0.29 (0.21) eV along the armchair (zigzag) direction, respectively, and an n-type lateral Schottky contact is established with the Cu electrode with an electron SBH of 0.64 (0.57) eV. Surprisingly, ML GeAs forms ideal p-type Ohmic contacts with the V2CF2 electrode. The results provide a theoretical foundation for comprehending the interactions between ML GeAs and metals, as well as for designing high-performance ML GeAs FETs.