Romans 6:3-11: "3 Do you not know that all of us who have been baptized into Christ Jesus were baptized into his death? 4 We were buried therefore with him by baptism into death, in order that, just as Christ was raised from the dead by the glory of the Father, we too might walk in newness of life.
"5 For if we have been united with him in a death like his, we shall certainly be united with him in a resurrection like his. 6 We know that our old self was crucified with him in order that the body of sin might be brought to nothing, so that we would no longer be enslaved to sin. 7 For one who has died has been set free from sin. 8 Now if we have died with Christ, we believe that we will also live with him. 9 We know that Christ, being raised from the dead, will never die again; death no longer has dominion over him. 10 For the death he died he died to sin, once for all, but the life he lives he lives to God. 11 So you also must consider yourselves dead to sin and alive to God in Christ Jesus."
John 3:1-6: "1 Now there was a man of the Pharisees named Nicodemus, a ruler of the Jews. 2 This man came to Jesus by night and said to him, 'Rabbi, we know that you are a teacher come from God, for no one can do these signs that you do unless God is with him.' 3 Jesus answered him, 'Truly, truly, I say to you, unless one is born again he cannot see the kingdom of God.' 4 Nicodemus said to him, 'How can a man be born when he is old? Can he enter a second time into his mother's womb and be born?' 5 Jesus answered, 'Truly, truly, I say to you, unless one is born of water and the Spirit, he cannot enter the kingdom of God. 6 That which is born of the flesh is flesh, and that which is born of the Spirit is spirit.'"
Romans 8:11: "If the Spirit of him who raised Jesus from the dead dwells in you, he who raised Christ Jesus from the dead will also give life to your mortal bodies through his Spirit who dwells in you."
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The text from Romans 6 is the main source for the hymn. The first line of the hymn is taken directly from verse 9.
The text from John 3, particularly verses 3-5, seems to appear in the line "Reborn, we share with Him an Easter life" in the second verse. While Romans 8:11 overlaps a bit with the text from Romans 6, it could be cited for this line too.