In the topographic complex catchments, landscape features have a significant impact on the spatial prediction of rainfall and temperature. In this study, performance assessments were made of various interpolation techniques for the prediction of the spatial distribution of rainfall and temperature in the Mille and Akaki River catchments, Ethiopia, through an improved approach on selecting the auxiliary variables as a covariate. Two geostatistical interpolation techniques, ordinary kriging (OK) and kriging with external drift (KED), and one deterministic interpolation technique, inverse distance weighting (IDW), were tested through a leave-one-out cross-validation (LOOCV) procedure. The results indicated that using the multivariate geostatistical interpolation technique (KED) with the auxiliary variables as a covariate outperformed the univariate geostatistical (OK) and deterministic (IDW) techniques for the spatial interpolation of sampled rainfall–temperature data in both contrasting catchments, Akaki and Mille, with the lowest estimation errors (e.g., for Mille annual mean rainfall: root mean square error=75.32, 77.34, 245.72, mean bias error=3.70, −33.18, −15.61, mean absolute error=67.99, 69.51, 192.64) using KED with the combination of elevation and easting as a covariate, IDW and OK, respectively. Thus, the study confirmed that the use of elevation and easting/northing coordinates as predictors in geostatistical interpolation techniques could significantly improve the spatial prediction of climatic variables.