We present the Voigt profile (VP) models, column densities, Doppler b parameters, kinematics, and distribution of components for 422 MgII absorbers found in a survey of 249 HIRES and UVES quasar spectra. The equivalent width range of the sample is 0.006<~W_r_(2796)<~6.23{AA} and the redshift range is 0.19<~z<~2.55, with a mean of <z>=1.18. Based on historical precedent, we classified 180 absorbers as weak systems (W_r_(2796)<0.3{AA}) and 242 as strong systems (W_r_(2796)>~0.3{AA}). Assuming a minimum number of significant components per system, the VP fitting, yielded a total of 2989 components, with an average of 2.7 and 10.3 components found for the weak and strong MgII subsamples, respectively. The VP component line density for the full sample is 8.62{+/-}0.23clouds/{AA}. The distribution of VP component column density over the range 12.4<~logN(MgII)<~17.0/cm^2^ is well modeled with a power-law slope of -1.45{+/-}0.01. The median Doppler b parameters are 4.5{+/-}3.5km/s, 6.0{+/-}4.5km/s, and 5.7{+/-}4.4km/s for the weak, strong, and full samples. We modeled the probability of component velocity splitting (the two-point velocity correlation function) of our full sample using a three-component composite Gaussian function. Our resulting velocity dispersions are {sigma}_1_=25.4km/s, {sigma}_2_=68.7km/s, and {sigma}_3_=207.1km/s. These data provide an excellent database for studying the cosmic evolution of MgII absorber kinematic evolution.