Network function virtualization and multiaccess edge computing have been introduced by Internet service providers to deal with various challenges, which hinder them from satisfying the increasing demand of the low-latency network applications for the Internet of Things (IoT). In edge clouds, any network application for the IoT can be expressed as a service function chain (SFC) consisting of several strictly ordered virtual network functions (VNFs), which can be geographically placed onto edge clouds close to the terminals. However, regarding the large number of terminals and constantly dynamics of edge clouds, determining the placement of VNFs and routing service paths that optimizes the end-to-end delays is a challenging problem. This problem can be also called SFC dynamic orchestration problem. To exactly solve the problem, an integer linear programming (ILP) model is formulated. Then, it is difficult to apply the exact method to deal with the SFC dynamic orchestration problem in the large-scale networks, and this article presents a Lagrangian relaxation heuristic-based algorithm for the optimization, thus reducing the computational complexity. It is demonstrated that the proposed algorithm can efficiently achieve a near-optimal solution with a theoretical analysis. The obtained simulation results show that the proposed algorithm can approximate the performance of ILP’s solution and outperform the current benchmarks in terms of the end-to-end delay and service acceptance ratio.