We present and study a new mechanism of interaction between solitons based on the exchange interaction mediated by the localized fermion states. As particular examples, we consider solutions of simple ($1+1$)-dimensional scalar field theories with self-interaction potentials, including the sine-Gordon model and the polynomial ${\varphi }^4$ and ${\varphi }^6$ models, coupled to the Dirac fermions with a backreaction. We discover that there is an additional fermion exchange interaction between the solitons, and it leads to the formation of static multisoliton bound states. Furthermore, we argue that similar mechanisms of formation of stable coupled multisoliton configurations can be observed for a wide class of physical systems.