Acts 3:24-26: "'And all the prophets who have spoken, from Samuel and those who came after him, also proclaimed these days. You are the sons of the prophets and of the covenant that God made with your fathers, saying to Abraham, "And in your offspring shall all the families of the earth be blessed." God, having raised up his servant, sent him to you first, to bless you by turning every one of you from your wickedness.'"
Acts 13:32-33: "'And we bring you the good news that what God promised to the fathers, this he has fulfilled to us their children by raising Jesus, as also it is written in the second Psalm, "You are my Son, today I have begotten you."'"
Luke 24:27: "And beginning with Moses and all the Prophets, he [Jesus] interpreted to them in all the Scriptures the things concerning himself."
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The text is public domain:
Let the earth now praise the Lord,
Who has truly kept His word
And at last to us did send
Christ, the sinner's help and friend.
What the fathers most desired,
What the prophets' heart inspired,
What they longed for many a year,
Stands fulfilled in glory here.
Abram's promised great reward,
Zion's helper, Jacob's Lord -
Him of twofold race behold -
Truly came, as long foretold.
As Your coming was in peace,
Quiet, full of gentleness,
Let the same mind dwell in me
Which is Yours eternally.
Bruise for me the serpent's head
That, set free from doubt and dread,
I may cling to You in faith,
Safely kept through life and death.
Then when You will come again
As the glorious king to reign,
I with joy will see Your face,
Freely ransomed by Your grace.
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The first verse comes from the Acts 13 text. The hymn renders "what God promised to the fathers, this he has fulfilled to us their children by raising Jesus" as "the Lord / Who has truly kept His word / And at last to us did send / Christ..."
The second verse seems to come from the Luke text. In the Luke text, Jesus interprets what Moses and the prophets wrote "concerning himself," and the hymn verse mentions the same thing: that the fathers (which I'm assuming refers to the patriarchs) and the prophets "longed for" Jesus, who is "fulfilled in glory here."
The third verse, specifically "Abram's promised great reward," seems to come from the Acts 3 text, which also mentions "the covenant that God made with your fathers, ... to Abraham."
The rest of the verses don't seem to reference specific Biblical texts, aside from "Bruise for me the serpent's head" in verse five. It's not listed among the citations in the hymnal, but this is from Genesis 3:15. God says to the serpent, "I will put enmity between you and the woman, and between your offspring and her offspring; he shall bruise your head, and you shall bruise his heel."