Wheat grain yield (GY) is a crop feature of central importance affecting agricultural, environmental, and socioeconomic sustainability worldwide. Hence, the estimation of within-field variability of GY is pivotal for the agricultural management, especially in the current global change context. In this sense, Earth Observation Systems (EOS) are key technologies that use satellite data to monitor crop yield, which can guide the application of precision farming. Yet, novel research is required to improve the multiplatform integration of data, including data processing, and the application of this discipline in agricultural management. This article provides a novel methodological analysis and assessment of its applications in precision farming. It presents an integration of wheat GY, Global Positioning Systems (GPS), combine harvester data, and EOS Sentinel-2 multispectral bands. Moreover, it compares several indices and machine learning (ML) approaches to map within-field wheat GY. It also analyses the importance of multi-date remote sensing imagery and explores its potential applications in precision agriculture. The study was conducted in Spain, a major European wheat producer. Within-field GY data was obtained from a GPS combine harvester machine for 8 fields over three seasons (2017-2019) and consecutively processed to match Sentinel-2 10 m pixel size. Seven vegetation indices (NDVI, GNDVI, EVI, RVI, TGI, CVI and NGRDI) as well as the biophysical parameter LAI (leaf area index) retrieved with radiative transfer models (RTM) were calculated from Sentinel-2 bands. Sentinel-2 10 m resolution bands alone were also used as variables. Random forest, support vector machine and boosted regressions were used as modelling approaches, and multilinear regression was calculated as baseline. Different combinations of dates of measurement were tested to find the most suitable model feeding data. LAI retrieved from RTM had a slightly improved performance in estimating within-field GY in comparison with vegetation indices or Sentinel-2 bands alone. At validation, the use of multi-date Sentinel-2 data was found to be the most suitable in comparison with single date images. Thus, the model developed with random forest regression (e.g. R-2 = 0.89, and RSME = 0.74 t/ha when using LAI) outperformed support vector machine (R-2 = 0.84 and RSME = 0.92 t/ha), boosting regression (R-2 = 0.85 and RSME = 0.88 t/ha) and multilinear regression (R-2 = 0.69 and RSME = 1.29 t/ha). However, single date images at specific phenological stages (e.g. R-2 = 0.84, and RSME = 0.88 t/ha using random forest at stem elongation) also posed relatively high R-2 and low RMSE, with potential for precision farming management before harvest.