When did Spain become part of the Roman Empire?

Southern Spain was conquered by the Romans during the Second Punic War which lasted from 218 to 201 BC; Northern Spain was conquered by Augustus in 19 BC.

Yes, Spain was invaded by the Romans in 218 BCE. While the Romans did control most of the peninsula, they also had many native allies (much like the Europeans during the colonization era) the Romans had also established Lisbon, the capital of Portugal, and many others. When the Roman Empire collapsed, emperor Justinian the 1st of Byzantium had a short-lived control of Hispania and gave it a new name, Spania.