From Wiktionary

addict means:

A person who is addicted, especially to a harmful drug
An adherent or fan (of something)

Its etymology is:

ad- (“to, towards, at”) + dīcō (“say; declare”)

How does its meaning come from its etymology?

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Addict, v.: trans. Roman Law. To deliver or hand over formally (a person or thing) in accordance with a judicial decision

Addict, v. < Addict, adj. < classical Latin addīctus assigned by decree, made over, bound, devoted, past participle of addīcere to assign, to make over by sale or auction, to award, to appoint, to ascribe, to hand over, surrender, to enslave, to devote, to sentence, condemn < ad ad- prefix + dīcere to speak, say

Straight from the OED.

Another parsing of the same roots from the 'other' OED (the online etymological dictionary):

addict (v.) 1530s (implied in addicted), from Latin addictus, past participle of addicere "to deliver, award, yield; give assent, make over, sell," figuratively "to devote, consecrate; sacrifice, sell out, betray" from ad- "to" (see ad-) + dicere "say, declare" (see diction), but also "adjudge, allot." Earlier in English as an adjective, "delivered, devoted" (1520s). Related: Addicted; addicting.

Emphasis added.

http://www.etymonline.com/index.php?term=addict&allowed_in_frame=0

With a little google from my friends...

addictus, addicti : person enslaved for debt or theft

.

addictus
I
addicta -um, addictior -or -us, addictissimus -a -um ADJ
devoted/addicted (to); (debt) slave (of); bound (to do something); bent upon

II
addicti N M
person enslaved for debt or theft

Latin-English dictionary. 2013.

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For centuries, the word "addiction" meant being "given over" or devoted to something. However, the 19th century temperance and anti-opium movements used it in a more restrictive way, linking "addiction" to drugs, to illness or vice, and to withdrawal symptoms and tolerance. Both the traditional and restrictive meanings survived into the present. In the ensuing uncertainty about its meaning, some authorities now wish to replace "addiction" with substitute terms like "drug dependence", "substance abuse", etc. We hope to show that the term "addiction" is too valuable to discard. Its traditional sense designates the profoundly important, albeit sometimes harmful, capacity of people to become "given over." On the other hand, the restrictive meaning refers only to a special case, which is defined arbitrarily and inconsistently. It is outmoded because of these problems. The traditional meaning remains useful, but can be improved by clarifying the distinction between "positive" and "negative" addictions originally proposed by Glasser (1976). the paper in full

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The word addiction emerged from the Latin word addico, and is translated as, “of a judge, especially the praetor, to award a debtor as a slave to his creditor” (“addico,” 1968, p. 11, def. 2a). In a more general sense “to give oneself up too slavishly” (def. 3). addico is a compound build of ad (to, towards, at) and dico (say, affirm, tell). According to the Roman law, an addictio was a person who was enslaved through a judicial procedure. In the time of the Roman Empire, when a debtor could not repay his or her debt, creditors could recover their losses using a legal procedure. In that procedure, if proven that the debtor lacks the means to repay, the praetor, or the justice, could turn the debtor into a slave. Today the term addict is used to denote a person who is bonded, enslaved, with a substance or any other activity that is pleasurable. It is notable that the word addiction, used today to denote repeated consumption of drugs, or obsession with food, sex, or gambling, for example, is derived from a Latin word which expresses the slavery or bondage of a person. This connection will be further explored in Chapter III, where the story of Exodus, a story of breaking out from slavery, is used as an outline or scheme for recovery from addiction.

"Revisiting Addiction Using Depth Psychology: The Myth of Exodus as a Blueprint for Recovery" by Gil Simsic

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on the positive sense vs the negative sense of the term:
Encyclopaedia perthensis, or, Universal dictionary of the arts, sciences, literature, &c., 1816
THE AMERICAN DICTIONARY OF THE ENGLISH LANGUAGE, 1908

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ADDICT, ADDICTION [L. addico, addicere / to surrender to, give up] To give oneself up to an obsessive habit. To commit oneself to use of a habit- forming substance. To be incapable of withdrawing from compulsive use of a harmful substance. An addiction is a persisent, uncontrollable commitment to the use of drugs or other products known to be harmful.

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slavery in Roman law

A person might become a slave in various ways in consequence of positive law, Jure Civili. This was the case with Incensi [Caput], and those who evaded military service (Cic. pro Caecina, 34). In certain cases, a man became a slave, if he allowed himself to be sold as a slave in order to defraud the purchaser; and a free woman who cohabited with a slave might be reduced to the same condition [Senatusconsultum Claudianum.] Under the empire the rule was established that persons condemned to death, to the mines, and to fight with wild beasts, lost their freedom, and their property was confiscated, whence, concludes Gaius, it appears that they lose the Testamenti factio (Dig. 28 tit. 1 s8). But this was not the earlier law. A person so condemned, though he lost his freedom, had no master, and consequently the hereditates and legacies which were left to him, were simply void; for such a person was "poenae servus, non Caesaris" (Dig. 34 tit. 8 s3). A man never lost his freedom by usucapion (Gaius, II.48). According to the old law a manifestus fur was liable to a capitalis poena and was addicted (addicebatur) to the person whose property he had stolen; but it was doubted whether the effect of the addictio was to make him a servus or to put him in the condition of an adjudicatus (Gaius, III.189).

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Jane's Addiction (a rock band)

"I Would For You"

I'm everybody's slave
I made you my slave
...

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