The word “adoption” (Greek huiothesias) occurs only a few times in the New Testament, and each time it refers to God choosing a people for himself. Though there are not a lot of references to this word, there is a good deal we learn from them about the doctrine of adoption.
1) God adopts those whom he loves and has predestined to be his children
“In love he predestined us for adoption as sons through Jesus Christ, according to the purpose of his will, to the praise of his glorious grace” (Ephesians 1:4-6)
2) It is through Jesus Christ that God’s children are adopted
“In love he predestined us for adoption as sons through Jesus Christ, according to the purpose of his will, to the praise of his glorious grace” (Ephesians 1:4-6)
“But when the fullness of time had come, God sent forth his Son, born of woman, born under the law, to redeem those who were under the law, so that we might receive adoption as sons.” (Galatians 4:4-5)
3) God adopts his children so that he might display the glory of his grace
“In love he predestined us for adoption as sons through Jesus Christ, according to the purpose of his will, to the praise of his glorious grace” (Ephesians 1:4-6)
4) God has secured this adoption by his Spirit
“For you did not receive the spirit of slavery to fall back into fear, but you have received the Spirit of adoption as sons, by whom we cry, ‘Abba! Father!’” (Romans 8:15)
5) God will complete this adoption when he renews our bodies, thus making us eager for Christ’s return
“And not only the creation, but we ourselves, who have the firstfruits of the Spirit, groan inwardly as we wait eagerly for adoption as sons, the redemption of our bodies.” (Romans 8:23)
For more on the doctrine of adoption, I recommend Reclaiming Adoption, edited by Dan Cruver, or Adopted for Life by Russell Moore.