At present, it is critical to accurately monitor wheat crops to help decision-making processes in precision agriculture. This research aims to retrieve various wheat crop traits from hyperspectral data using machine learning regression algorithms (MLRAs) and dimensionality reduction (DR) techniques. This experiment was conducted in an agricultural field in Arborea, Oristano-Sardinia, Italy, with different factors such as cultivars, N-treatments, and soil ploughing conditions. Hyperspectral data were acquired on the ground using a full-range Spectral Evolution spectrometer (350–2500 nm). Four DR techniques, including (i) variable influence on projection (VIP), (ii) principal component analysis (PCA), (iii) vegetation indices (VIs), and (iv) spectroscopic feature (SF) calculation, were undertaken to reduce the dimension of the hyperspectral data while maintaining the information content. We used five MLRA models, including (i) partial least squares regression (PLSR), (ii) random forest (RF), (iii) support vector regression (SVR), (iv) Gaussian process regression (GPR), and (v) neural network (NN), to retrieve wheat traits at either leaf and canopy levels. The studied traits were leaf area index (LAI), leaf and canopy water content (LWC and CWC), leaf and canopy chlorophyll content (LCC and CCC), and leaf and canopy nitrogen content (LNC and CNC). MLRA models were able to accurately retrieve wheat traits at the canopy level with PLSR and NN indicating the highest modelling performance. On the contrary, MLRA models indicated less accurate retrievals of the leaf-level traits. DR techniques were found to notably improve the retrieval accuracy of crop traits. Furthermore, the generated models were re-calibrated using soil spectra and then transferred to an airborne dataset collected using a CASI-SASI hyperspectral sensor, allowing the estimation of wheat traits across the entire field. The predicted crop trait maps illustrated consistent patterns while also preserving the real-field characteristics well. Lastly, a statistical paired t-test was undertaken to conduct a proof of concept of wheat phenotyping analysis considering the different agricultural variables across the study site. N-treatment caused significant differences in wheat crop traits in many instances, whereas the observed differences were less pronounced between the cultivars. No particular impact of soil ploughing conditions on wheat crop characteristics was found. Using such combinations of MLRA and DR techniques based on hyperspectral data can help to effectively monitor crop traits throughout the cropping seasons and can also be readily applied to other agricultural settings to help both precision farming applications and the implementation of high-throughput phenotyping solutions.