Novel time-harmonic beam fields have been recently obtained by utilizing a non-orthogonal coordinate system which is a priori matched to the field's planar linearly-phased Gaussian aperture distribution. These waveobjects were termed tilted Gaussian beams. The present investigation is concerned with parameterization of these time-harmonic tilted Gaussian beams and of the wave phenomena associated with them. Specific types of tilted Gaussian beams that are characterized by their aperture complex curvature matrices, are parameterized in term of beam-widths, waist-locations, collimation-lengths, radii of curvature, and other features. Emphasis is placed on the difference in the parameterization between the conventional (orthogonal coordinates) beams and the tilted ones.