1530s, "delivered over" by judicial sentence; past participle adjective from addict (v.). Modern sense of "dependent" is short for self-addicted "to give over or award (oneself) to someone or some practice" (1560s; exact phrase from c. 1600); specialization to narcotics dependency is from c. 1910.
1. I went through about four years of being addicted to video games.
2. Many of the women are addicted to heroin and cocaine.
3. After about three months, I was no longer addicted to nicotine.