Colossians 3:12-14: "12 Put on then, as God's chosen ones, holy and beloved, compassionate hearts, kindness, humility, meekness, and patience, 13 bearing with one another and, if one has a complaint against another, forgiving each other; as the Lord has forgiven you, so you also must forgive. 14 And above all these put on love, which binds everything together in perfect harmony."
Ephesians 5:2: "And walk in love, as Christ loved us and gave himself up for us, a fragrant offering and sacrifice to God."
1 Corinthians 13: "1 If I speak in the tongues of men and of angels, but have no love, I am a noisy gong or a clanging cymbal. 2 And if I have prophetic powers, and understand all mysteries and all knowledge, and if I have all faith, so as to remove mountains, but have not love, I am nothing. 3 If I give away all I have, and if I deliver up my body to be burned, but have no love, I gain nothing.
"4 Love is patient and kind; love does not envy or boast; it is not arrogant 5 or rude. It does not insist on its own way; it is not irritable or resentful; 6 it does not rejoice at wrongdoing, but rejoices with the truth. 7 Love bears all things, believes all things, hopes all things, endures all things.
"8 Love never ends. As for prophecies, they will pass away; as for tongues, they will cease; as for knowledge, it will pass away. 9 For we know in part and we prophesy in part, 10 but when the perfect comes, the partial will pass away. 11 When I was a child, I spoke like a child, I thought like a child, I reasoned like a child. When I became a man, I gave up childish ways. 12 For now we see in a mirror dimly, but then face to face. Now I know in part; then I shall know fully, even as I have been fully known.
"13 So now faith, hope, and love abide, these three; but the greatest of these is love."
Ephesians 4:2: "with all humility and gentleness, with patience, bearing with one another in love"
Ephesians 4:32: "Be kind to one another, tenderhearted, forgiving one another, as God in Christ forgave you."
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All but the last cited text mention love, and so there's quite a bit of overlap, but there are parts of the hymn that clearly come from one text more than an-other.
The line "Binding faithful hearts in one" in the first verse comes from Colossians 3:14. The line "May His will in us be done" at the end of the verse seems to be patterned on "Thy will be done" in the Lord's Prayer (Matthew 6:10), although in the hymn, the "His" is referring to Christ where in the Lord's Prayer, the "Thy" refers to God the Father. Taken together with the preceding line ("Love in Christ is true and giving"), this may come from Ephesians 5:2.
The second verse contains a list of love's attributes and combines qualities from 1 Corinthians 13 (particularly verse 4), Colossians 3:12-13, and the two verses from Ephesians 4.
The line "Love in Christ abides forever" at the beginning of the third verse comes from 1 Corinthians 13 (apparently combining parts of verses 8 and 13), and the line "Love, forgiving and forgiven" from later in the verse combines Colossians 3:13 and Ephesians 4:32.