Emerging Internet of Things (IoT)/Machine-to-Machine (M2M) systems require a transparent access to information and services through a seamless integration into the Future Internet. This integration exploits infrastructure and services found on the Internet by the IoT. On the one hand, the so-called Web of Things aims for direct Web connectivity by pushing its technology down to devices and smart things. On the other hand, the current and Future Internet offer stable, scalable, extensive, and tested protocols for node and service discovery, mobility, security, and auto-configuration, which are also required for the IoT. In order to integrate the IoT into the Internet, this work adapts, extends, and bridges using IPv6 the existing IoT building blocks (such as solutions from IEEE 802.15.4, BT-LE, RFID) while maintaining backwards compatibility with legacy networked embedded systems from building and industrial automation. Specifically, this work presents an extended Internet stack with a set of adaptation layers from non-IP towards the IPv6-based network layer in order to enable homogeneous access for applications and services.