Remote sensing has been recognized as the main technique to extract land cover/land use (LC/LU) data, required to address many environmental issues. Therefore, over the years, many approaches have been introduced and explored to optimize the resultant classification maps. Particularly, index-based methods have highlighted its efficiency and effectiveness in detecting LC/LU in a multitemporal and multisensors analysis perspective. Nevertheless, the developed indices are suitable to extract a specific class but not to completely classify the whole area. In this study, a new Landsat Images Classification Algorithm (LICA) is proposed to automatically detect land cover (LC) information using satellite open data provided by different Landsat missions in order to perform a multitemporal and multisensors analysis. All the steps of the proposed method were implemented within Google Earth Engine (GEE) to automatize the procedure, manage geospatial big data, and quickly extract land cover information. The algorithm was tested on the experimental site of Siponto, a historic municipality located in Apulia Region (Southern Italy) using 12 radiometrically and atmospherically corrected satellite images collected from Landsat archive (four images, one for each season, were selected from Landsat 5, 7, and 8, respectively). Those images were initially used to assess the performance of 82 traditional spectral indices. Since their classification accuracy and the number of identified LC categories were not satisfying, an analysis of the different spectral signatures existing in the study area was also performed, generating a new algorithm based on the sequential application of two new indices (SwirTirRed (STRed) index and SwiRed index). The former was based on the integration of shortwave infrared (SWIR), thermal infrared (TIR), and red bands, whereas the latter featured a combination of SWIR and red bands. The performance of LICA was preferable to those of conventional indices both in terms of accuracy and extracted classes number (water, dense and sparse vegetation, mining areas, built-up areas versus water, and dense and sparse vegetation). GEE platform allowed us to go beyond desktop system limitations, reducing acquisition and processing times for geospatial big data.