Final answer:
Claudius is the emperor who added Britain to the Roman State.
Step-by-step explanation:
The emperor who finally added Britain to the Roman State was Claudius.
Claudius became emperor in 41 CE after the assassination of his nephew Caligula. He was an effective ruler and during his reign, Britain was added to the Roman empire.
This expansion was significant as it provided the Romans with access to valuable resources and control over trade routes.