Network function virtualisation (NFV), software defined networks (SDNs), and mobile edge computing (MEC) are emerging as core technologies to satisfy increasing number of users' demands in 5G and beyond wireless networks. SDN provides clean separation of the control plane from the data plane while NFV enables the flexible and on‐the‐fly creation and placement of virtual network functions (VNFs) and are able to be executed within the various locations of a distributed system. In this paper, VNF placement and resource allocation (VNFPRA) problem is considered which involves placing VNFs optimally in distributed NFV‐enabled MEC nodes and assigning MEC resources efficiently to these VNFs to satisfy users' requests in the network. Current solutions to this problem are slow and cannot handle real‐time requests. To this end, an SDN‐NFV infrastructure is proposed to tackle the VNFPRA problem in wireless MEC networks. Our aim is to minimise the overall placement and resource cost and also to minimise the total number of VNF migrations. A genetic based heuristic algorithm is proposed. The superior performance of the proposed solution is confirmed in comparison with four existing algorithms, i.e. resource utilisation‐single objective evolutionary algorithm (RU‐SOEA), genetic non‐bandwidth link allocation algorithm (GA‐NBA), random‐fit placement algorithm (RFPA), and first‐fit placement algorithm (FFPA). The results demonstrate that a coordinated placement of VNFs in SDN/NFV enabled MEC networks can satisfy the objective of overall reduced cost. Simulation results also reveal that the proposed scheme approximates well with the optimal solution returned by Gurobi and also achieves reduction on overall cost compared to other methods.