The incorporation of Wireless Local Area Networks (WLANs) within the third generation (3G) networks materializes the next generation of mobile/wireless systems, named 3G-WLANs integrated networks. This paper proposes an improved authentication procedure for the 3G-WLANs integrated networks that enables a WLAN user to get access to the 3G packet switched services or to the public Internet through the 3G public land mobile network. The proposed procedure reduces significantly the authentication overhead compared to the legacy one, without compromising the provided security services. A security analysis of the proposed authentication procedure is elaborated that ensures the correctness of the authentication procedure, the provision of advanced security services and the elimination of possible attacks that may threaten the proposed authentication procedure. In addition, an energy cost analysis is carried out that compares the energy consumption induced by the legacy and the proposed authentication procedures. Finally, a communication cost analysis is provided that estimates the cost improvement of the proposed over the legacy authentication procedure.