Biblical definition for addiction is to practice sin to the point that it becomes a stronghold and idolatrous.  A stronghold; a power over us, and idolatrous; loving it so much we are not willing to give it up for God.    

The Word of God speaks plainly to those who are willing to hear:

Addiction is the sowing to our flesh and at not the Spirit.  Romans 8:1-8

Addiction reveals our spiritual condition which is dead in our sins being held captive by them. Eph 2:1-3

Those caught in addiction offer their bodies (as a sacrifice) to whatever idol they are bound to. Romans 12:1

Those who live after their lusts (addiction) are loving and serving another.  Matt 6:24

When anyone loves themselves and the world’s (addictions) the love of the Father is not in them; 1 John 2:15-16

Addiction is sowing to the flesh and reaping corruption; Gal 6:7-8

Addiction is disobedience to the Word and God’s will for us. 1 Pet 4:1-5

The use of drugs or alcohol that alters the state of mind, or ‘puts you under the influence’ is what the bible refers to as sorcery.

Addiction is the works of the flesh, and those who practice such works will not inherit the Kingdom of God.  1 Cor 6:9-10, Gal 5:19-21 Rev 22:14-15

See also these posts regarding Addiction.