The portable devices such as mobile phones, laptops or personal digital assistants (PDAs) are used by mobile ad hoc networks (MANETs) for communication establishment in a spontaneous manner. For fulfilling the coverage requirements of future 4G we need integration of mobile ad hoc network with Internet to enhance the pervasiveness and flexibility of networks. It is necessary for mobile nodes to identify and choose an optimal gateway among multiple gateways for Internet access. Therefore, a mechanism for gateway discovery is needed. The adaptive gateway discovery can be configured by dynamically adjusting its TTL value (proactive area) on the basis of several parameters like number of active source nodes, traffic load at the gateway and link changes. Existing schemes involve inaccurate estimation of optimal proactive area, hence they suffer from large routing overhead which ultimately affects the network performance and throughput. This paper aims to develop a novel and efficient adaptive gateway discovery algorithm focusing on optimal TTL value by utilizing the potential and capability of Fuzzy logic, which makes a significant impact on routing overhead during gateway discovery. The proposed scheme also incorporates efficient handover in the situation of multiple gateways so that single gateway will not become a bottleneck. The proposed approach is evaluated using computer simulation and also analytically validated. Results show our approach outperforming existing ones.