The promising connected vehicle technologies will enable a huge network of roadside units (RSUs) and vehicles equipped with communication, computing, storage, and positioning devices. Current research on connected vehicle networks focuses on delivering the data generated from or required by the vehicle networks themselves, of which the data traffic is light; thus, the vehicle-network resource utilization efficiency is low. On the other hand, a large amount of delay-tolerant traffic in other data networks consumes significant communication resources. In this paper, we introduce a new architecture of DaVe to utilize efficiently the potential resource from connected vehicles and to mitigate the congestion problem in other data networks. Delay-tolerant data traffic is offloaded from the data networks to the connected vehicle networks without extra infrastructure/hardware deployment. An optimal distributed data hopping mechanism is also proposed to enable delay-tolerant data routing over connected vehicle networks. We formulate the next-hop decision optimization problem as a partially observable Markov decision process (POMDP) and propose a heuristic algorithm to reduce computational complexity. Extensive simulation results are also presented to demonstrate the significant performance improvement of the proposed scheme.