Conventional Internet of Things (IoT) applications involve data capture from various sensors in environments, and the captured data then is processed in remote clouds. However, some critical IoT applications (e.g., autonomous vehicles) require a much lower response latency and more secure guarantees than those offered by remote clouds today. Mobile edge clouds (MEC) supported by the network function virtualization (NFV) technique have been envisioned as an ideal platform for supporting such IoT applications. Specifically, MECs enable to handle IoT applications in edge networks to shorten network latency, and NFV enables agile and low-cost network functions to run in low-cost commodity servers as virtual machines (VMs). One fundamental problem for the provisioning of IoT applications in an NFV-enabled MEC is where to place virtualized network functions (VNFs) for IoT applications in the MEC, such that the operational cost of provisioning IoT applications is minimized. In this paper, we first address this fundamental problem, by considering a special case of the IoT application placement problem, where the IoT application and VNFs of each service request are consolidated into a single location (gateway or cloudlet), for which we propose an exact solution and an approximation algorithm with a provable approximation ratio. We then develop a heuristic algorithm that controls the resource violation ratios of edge clouds in the network. For the IoT application placement problem for IoT applications where their VNFs can be placed to multiple locations, we propose an efficient heuristic that jointly places the IoT application and its VNFs. We finally study the performance of the proposed algorithms by simulations and implementations in a real test-bed, Experimental results show that the performance of the proposed algorithms outperform their counterparts by at least 10 percent.