Linker histones bind to nucleosomes and modify chromatin structure and dynamics as a means of epigenetic regulation. Biophysical studies have shown that chromatin fibers can adopt a plethora of conformations with varying levels of compaction. Linker histone condensation, and its specific binding disposition, has been associated with directly tuning this ensemble of states. However, the atomistic dynamics and quantification of this mechanism remains poorly understood. Here, we present molecular dynamics simulations of octa-nucleosome arrays, based on a cryo-EM structure of the 30-nm chromatin fiber, with and without the globular domains of the H1 linker histone to determine how they influence fiber structures and dynamics. Results show that when bound, linker histones inhibit DNA flexibility and stabilize repeating tetra-nucleosomal units, giving rise to increased chromatin compaction. Furthermore, upon the removal of H1, there is a significant destabilization of this compact structure as the fiber adopts less strained and untwisted states. Interestingly, linker DNA sampling in the octa-nucleosome is exaggerated compared to its mono-nucleosome counterparts, suggesting that chromatin architecture plays a significant role in DNA strain even in the absence of linker histones. Moreover, H1-bound states are shown to have increased stiffness within tetra-nucleosomes, but not between them. This increased stiffness leads to stronger long-range correlations within the fiber, which may result in the propagation of epigenetic signals over longer spatial ranges. These simulations highlight the effects of linker histone binding on the internal dynamics and global structure of poly-nucleosome arrays, while providing physical insight into a mechanism of chromatin compaction.