Final answer:
The Network Layer is responsible for accepting outgoing messages and combining them into packets, adding a header with routing information.
Step-by-step explanation:
The layer of the OSI model that accepts outgoing messages and combines them into packets, adding a header with routing information is the Network Layer. This layer is responsible for logical addressing and routing of data across different networks, enabling communication between devices. It determines the best path for data to reach its destination and adds the necessary information to the packets.