Lateral mesoscale eddy-induced tracer transport is traditionally represented in coarse-resolution models by the flux–gradient relation. In its most complete form, the relation assumes the eddy tracer flux as a product of the large-scale tracer concentration gradient and an eddy transport coefficient tensor. However, several recent studies reported that the tensor has significant spatiotemporal complexity and is not uniquely defined, that is, it is sensitive to the tracer distributions and to the presence of nondivergent (“rotational”) components of the eddy flux. These issues could lead to significant biases in the representation of the eddy-induced transport. Using a high-resolution tracer model of the Gulf Stream region, we examine the diffusive and advective properties of lateral eddy-induced transport of dynamically passive tracers, reevaluate the utility of the flux–gradient relation, and propose an alternative approach based on modeling the local eddy forcing by a combination of diffusion and generalized eddy-induced advection. Mesoscale eddies are defined by a scale-based spatial filtering, which leads to the importance of new eddy-induced terms, including eddy-mean covariances in the eddy fluxes. The results show that the biases in representing these terms are noticeably reduced by the new approach. A series of targeted simulations in the high-resolution model further demonstrates that the approach outperforms the flux–gradient model in reproducing the stirring and dispersing effect of eddies. Our study indicates potential to upgrade the traditional flux–gradient relation for representing the eddy-induced tracer transport.