Vehicular ad hoc networks (VANETs) have been identified as a key technology to enable intelligent transport systems (ITS), which are aimed to radically improve the safety, comfort, and greenness of the vehicles in the road. However, in order to fully exploit VANETs potential, several issues must be addressed. Because of the high dynamic of VANETs and the impairments in the wireless channel, one key issue arising when working with VANETs is the multihop dissemination of broadcast packets for safety and infotainment applications. In this paper a reliable low-overhead multihop broadcast (RLMB) protocol is proposed to address the well-known broadcast storm problem. The proposed RLMB takes advantage of the hello messages exchanged between the vehicles and it processes such information to intelligently select a relay set and reduce the redundant broadcast. Additionally, to reduce the hello messages rate dependency, RLMB uses a point-to-zone link evaluation approach. RLMB performance is compared with one of the leading multihop broadcast protocols existing to date. Performance metrics show that our RLMB solution outperforms the leading protocol in terms of important metrics such as packet dissemination ratio, overhead, and delay.