Heterogeneous networks are designed to offload or route some of data traffics of mobile networks through other co‐located wireless access networks. This technique apparently increases the capacity of mobile network. In such networks, a vertical handover process plays an important role in providing seamless and uninterrupted connectivity as well as the required level of quality‐of‐service along with a wide coverage for all mobile nodes. Traditional vertical handover algorithms that are based on single criterion (eg, received signal strength) are not performing well in terms of excess handover rates, ping‐pong effects, handover delays, handover cost, etc. This research presents an efficient multicriteria‐based vertical handover decision‐making algorithm for heterogeneous networks. This algorithm uses a two‐step execution procedure, the first step evaluates whether the handover is needed or not before initiating a handover process, if needed, then a set of feasible solutions are generated for the vertical handover problem formulated as a multi‐objective optimization problem with two objective functions such as quality factor of networks and handover processing cost. In the second step, an optimal solution (ie, an appropriate access network) for handover is obtained using a hybrid approach of fuzzy analytic hierarchy process (FAHP) and technique for order preference by similarity to ideal solution (TOPSIS). Our simulation study shows that the proposed algorithm performs well as compared to some other existing algorithms (ie, single‐criterion based, multicriteria with AHP, multicriteria with TOPSIS, and multicriteria with both AHP and TOPSIS) in terms of performance metrics such as handover rate, delay, cost, and energy consumption.