Q: What is adoption?
A: Adoption is an act of God's free grace, whereby we are received into the number, and have a right to all the privileges of the sons of God.

1 John 3:1. Behold, what manner of love the Father hath bestowed upon us, that we should be called the sons of God: therefore the world knoweth us not, because it knew him not.
John 1:12. But as many as received him, to them gave he power to become the sons of God, even to them that believe on his name.
Romans 8:17. And if children, then heirs; heirs of God, and joint-heirs with Christ; if so be that we suffer with him, that we may be also glorified together.

Westminster Project - See Francis Beattie further commentary on  adoption and sanctification as the benefits of Redemption