We present a combined experimental and theoretical study of the interplay between the atomic structure and the magnon excitations in low dimensional ferromagnets. Two monolayer thick Fe films on W(110) with and without a Au buffer layer are investigated. Our experiments show that adding the Au layer leads to a significant softening of the magnons. First-principles calculations confirm the experimental results revealing a strong dependency of exchange interactions on the atomic structure. It is observed that the intralayer exchange interactions increase with increasing distance between Fe layers. This unusual relationship is attributed to the complexity of the electronic structure and the contribution of different orbitals to the hybridization and exchange interaction. Our results suggest a way of tailoring magnetic excitations in low-dimensional magnetic structures.