From BelieveTheSign

God is the Redeemer of mankind. The meaning of redeem is to buy, or purchase, in order to receive power over an object that was formerly the power of another. In the Old Testament, certain things could only be redeemed by a Kinsman, and were redeemed as a 'take everything' or 'leave everything' package. For example, the man Boaz wanted to take the widow Ruth as his wife, but as there was a closer Kinsman, he had to make an agreement with that Kinsman first. The other Kinsman wanted the land that came with redeeming Ruth, but did not want to redeem Ruth (which would have required him to have children with her), so he forfeit the right to redeem the land by refusing to redeem Ruth. Boaz then inherited Ruth and the land.

In the New Testament, Jesus Christ became a kinsman by being made under the law in the form of a man. He then became our redeemer through the shedding of his blood for our sins.

"Redeemer" in the Old Testament

Scripture Name Meaning
Job 19:25 Haggo’el Redeemer
Leviticus 25:26 Go’el Kinsman Redeemer
Isaiah 49:7 Go’el Israel Redeemer of Israel
Psalms 19:14 Jehovah tsuri v’goali The LORD my strength and redeemer

"Redeemer" in the New Testament

Scripture Text:
LUKE 1:67-69 And his father Zacharias was filled with the Holy Ghost, and prophesied, saying, Blessed be the Lord God of Israel; for he hath visited and redeemed his people, And hath raised up an horn of salvation for us in the house of his servant David;
LUKE 24:19-21 And he said unto them, What things? And they said unto him, Concerning Jesus of Nazareth, which was a prophet mighty in deed and word before God and all the people: And how the chief priests and our rulers delivered him to be condemned to death, and have crucified him. But we trusted that it had been he which should have redeemed Israel: and beside all this, to day is the third day since these things were done.
GALATIANS 3:13 Christ hath redeemed us from the curse of the law, being made a curse for us: for it is written, Cursed is every one that hangeth on a tree:
GALATIANS 4:4-5 But when the fulness of the time was come, God sent forth his Son, made of a woman, made under the law, To redeem them that were under the law, that we might receive the adoption of sons.
EPHESIANS 5:15-16 See then that ye walk circumspectly, not as fools, but as wise, Redeeming the time, because the days are evil.
COLOSSIANS 4:5 Walk in wisdom toward them that are without, redeeming the time.
TITUS 2:13-14 Looking for that blessed hope, and the glorious appearing of the great God and our Saviour Jesus Christ; Who gave himself for us, that he might redeem us from all iniquity, and purify unto himself a peculiar people, zealous of good works.
I PETER 1:18-19 Forasmuch as ye know that ye were not redeemed with corruptible things, as silver and gold, from your vain conversation received by tradition from your fathers; But with the precious blood of Christ, as of a lamb without blemish and without spot:
REVELATION 5:8-9 And when he had taken the book, the four beasts and four and twenty elders fell down before the Lamb, having every one of them harps, and golden vials full of odours, which are the prayers of saints. And they sung a new song, saying, Thou art worthy to take the book, and to open the seals thereof: for thou wast slain, and hast redeemed us to God by thy blood out of every kindred, and tongue, and people, and nation;
REVELATION 14:3-4 And they sung as it were a new song before the throne, and before the four beasts, and the elders: and no man could learn that song but the hundred and forty and four thousand, which were redeemed from the earth. These are they which were not defiled with women; for they are virgins. These are they which follow the Lamb whithersoever he goeth. These were redeemed from among men, being the firstfruits unto God and to the Lamb.