Considered as part of the Internet of Things (IoT) concept, Internet-connected wireless sensor networks (WSNs) are increasingly using sensor nodes with mobility option. The mobility of sensor nodes is not necessarily limited within a single WSN but could also be across several WSNs. From this, efficiency, flexibility, and interoperability with the existing infrastructure are mandatory features. Unfortunately, current mobility management solutions are not optimized sufficiently for WSNs. In this paper, we propose a new solution (named as CL-MIPv6) that uses detected link-layer information with an adapted scheme of the standard MIPv6 to provide constrained mobile nodes with fast, reliable, and low-cost internetwork handoffs. The idea behind our proposal consists of enabling reliable internetwork mobility anticipation, fast foreign-network detection, and then processing low-overhead handoff-related signaling at mobile nodes. The evaluation of the proposed solution has demonstrated remarkable improvements in terms of reliability and energy-latency costs of internetwork handoffs. The advantage of the contribution over its counterparts becomes more significant as the mobility speed and the overall network traffic load increase.