This paper presents the constitutive modeling of the flexomagnetic (FM) effect in structures involving a non-zero magnetic field generated in the presence of inhomogeneous strain across the domain. In order to evaluate the magneto-elastic (ME) structural response, the tensorial governing equations and associated boundary conditions for the mechanical and magnetic variables are derived here using the variational principle. Following this, these differential equations are solved to determine the effect of FM over the bending response of a cantilever piezomagnetic nanobeam. Different magnetic boundary conditions are analyzed to study the effect of direct and converse FM couplings over the ME response. The significant influence of FM coupling over the ME response has been noted for thin beams with low-dimensions, which wanes as the geometric dimensions are increased. Given the significance of this size-dependent FM response in nano-structures, the theory for flexomagnetism proposed here may be utilized in the development of smart ME nano-structures with the potential for wide applications. © 2018 Author(s).