Driven by digitization in society and industry, automating behavior in an autonomous way substantially alters industrial value chains in the smart service world. As processes are enhanced with sensor and actuator technology, they become digitally interconnected and merge into an Internet of Things (IoT) to form cyber-physical systems (CPS). Using these automated systems, enterprises can improve the performance and quality of their operations. However, currently it is neither feasible nor reasonable to equip any machine with full autonomy when networking with other machines or people. It is necessary to specify rules for machine behavior that also determine an adequate degree of autonomy to realize the potential benefits of the IoT. Yet, there is a lack of methodologies and guidelines to support the design and implementation of machines as explicit autonomous agents such that many designs only consider autonomy implicitly. To address this research gap, we perform a comprehensive literature review to extract 12 requirements for the design of autonomous agents in the IoT. We introduce a set of constitutive characteristics for agents and introduce a classification framework for interactions in multi-agent systems. We integrate our findings by developing a conceptual modeling language consisting of a meta model and a notation that facilitates the specification and design of autonomous agents within the IoT as well as CPS: the Autonomy Model and Notation. We illustrate and discuss the approach and its limitations.