Telomeres are specialized nucleoprotein assemblies that protect the ends of linear chromosomes. In humans and many other species, telomeres consist of tandem TTAGGG repeats bound by a protein complex known as shelterin that remodels telomeric DNA into a protective loop structure and regulates telomere homeostasis. Shelterin recognizes telomeric repeats through its two major components known as Telomere Repeat-Binding Factors, TRF1 and TRF2. These two homologous proteins are therefore essential for the formation and normal function of telomeres. Indeed, TRF1 and TRF2 are implicated in a plethora of different cellular functions and their depletion leads to telomere dysfunction with chromosomal fusions, followed by apoptotic cell death. More specifically, it was found that TRF1 acts as a negative regulator of telomere length, and TRF2 is involved in stabilizing the loop structure. Consequently, these proteins are of great interest, not only because of their key role in telomere maintenance and stability, but also as potential drug targets. In the current study, we investigated the molecular basis of telomeric sequence recognition by TRF1 and TRF2 and their DNA binding mechanism. We used molecular dynamics (MD) to calculate the free energy profiles for binding of TRFs to telomeric DNA. We found that the predicted binding free energies were in good agreement with experimental data. Further, different molecular determinants of binding, such as binding enthalpies and entropies, the hydrogen bonding pattern and changes in surface area, were analyzed to decompose and examine the overall binding free energies at the structural level. With this approach, we were able to draw conclusions regarding the consecutive stages of sequence-specific association, and propose a novel aspartate-dependent mechanism of sequence recognition. Finally, our work demonstrates the applicability of computational MD-based methods to studying protein-DNA interactions.