In this paper we propose a novel distributed algorithm for task assignment on heterogeneous networks. We consider a set of tasks with heterogeneous cost to be assigned to a set of nodes with heterogeneous execution speed and interconnected by a network with unknown topology represented by an undirected graph. Our objective is to minimize the execution time of the set of tasks by the networked system. We propose a local interaction rule which allows the nodes of a network to cooperatively assign tasks among themselves with a guaranteed performance with respect to the optimal assignment exploiting a gossip based randomized interaction scheme. We characterize the convergence properties of the proposed approach and provide simulation results.