With the advent of artificial intelligence and machine learning, various domains of science and engineering communities have leveraged data-driven surrogates to model complex systems through fusing numerous sources of information (data) from published papers, patents, open repositories, or other resources. However, not much attention has been paid to the differences in quality and comprehensiveness of the known and unknown underlying physical parameters of the information sources, which could have downstream implications during system optimization. Additionally, existing methods cannot fuse multi-source data into a single predictive model. Towards resolving this issue, a multi-source data fusion framework based on Latent Variable Gaussian Process (LVGP) is proposed. The individual data sources are tagged as a characteristic categorical variable that are mapped into a physically interpretable latent space, allowing the development of source-aware data fusion modeling. Additionally, a dissimilarity metric based on the latent variables of LVGP is introduced to study and understand the differences in the sources of data. The proposed approach is demonstrated on and analyzed through two mathematical and two materials science case studies. From the case studies, it is observed that compared to using single-source and source unaware machine learning models, the proposed multi-source data fusion framework can provide better predictions for sparse-data problems.