Eukaryotic double-stranded DNA achieves cellular compaction through several hierarchical levels of organization. First, DNA wraps around nucleosomes that comprise of two copies each of the positively charged core histones H2A, H2B, H3 and H4. The resulting "bead-on-a-string" nucleoprotein complex folds further at physiological salt, and in the presence the linker histone, into the 30-nm chromatin fiber. The thermodynamic and structural details of how histone tails (N-termini of core histones) and linker histones critically compact and modulate chromatin structure as well as regulate gene transcription are not well understood. I present a new mesoscopic model of chromatin that represents nucleosome cores as rigid bodies with an electrostatic surface, linker DNA as a discrete worm-like chain model, and histone tails as protein bead chains, to elucidate the physical role of each histone tail and the linker histone in chromatin folding. An end-transfer configurational-bias Monte Carlo approach provides the positional distribution of histone tail and their physical interactions at different salt milieus. Analyses indicate that the H4 tails mediate the strongest internucleosomal interactions; the H3 tails crucially screen electrostatic repulsion between the linker DNAs; and the H2A and H2B tails mediate fiber/fiber interactions. The primary function of the linker histones is to decrease the nucleosome triple angles, resulting in highly compact chromatin with a different internucleosomal interaction pattern than that obtained in linker-histone deficient chromatin. The development of this model also opens new avenues for studying higher-order structures of chromatin and the role of posttranslational modifications and variants of histone tails in gene regulation.