Isaiah 40:1-8: "Comfort, comfort my people, says your God. Speak tenderly to Jerusalem, and cry to her that her warfare is ended, that her iniquity is pardoned, that she has received from the LORD's hand double for all her sins. A voice cries: 'In the wilderness prepare the way of the LORD; make straight in the desert a highway for our God. Every valley shall be lifted up, and every mountain and hill be made low; the uneven ground shall become level, and the rough places a plain. And the glory of the LORD shall be revealed, and all flesh shall see it together, for the mouth of the LORD has spoken.' A voice says, 'Cry!' And I said, 'What shall I cry?' All flesh is grass, and all its beauty is like the flower of the field. The grass withers, the flower fades when the breath of the LORD blows on it; surely the people are grass. The grass withers, the flower fades, but the word of our God will stand forever."
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The text is public domain:
"Comfort, comfort ye My people,
Speak ye peace," thus saith our God;
"Comfort those who sit in darkness,
Mourning 'neath their sorrows' load.
Speak ye to Jerusalem
Of the peace that waits for them;
Tell her that her sins I cover
And her warfare now is over."
Yea, her sins our God will pardon,
Blotting out each dark misdeed;
All that well deserved His anger
He no more will see or heed.
She hath suffered many a day,
Now her griefs have passed away;
God will change her pining sadness
Into everspringing gladness.
Hark, the herald's voice is crying
In the desert far and near,
Calling sinners to repentance,
Since the Kingdom now is here.
O that warning cry obey!
Now prepare for God a way;
Let the valleys rise to meet Him
And that hills bow down to greet Him.
Make ye straight what long was crooked;
Make the rougher places plain.
Let your hearts be true and humble,
As befits His holy reign.
For the glory of the Lord
Now o'er earth is shed abroad,
And all flesh shall see the token
That His Word is never broken.
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Unsurprisingly, the majority of the hymn text comes from the selection from Isaiah, which is the only Biblical text cited.
The lines "Calling sinners to repentance, / Since the Kingdom now is here" in the third verse seem to come from Matthew 3:2, where John the Baptist - to whom the Isaiah text refers - says, "Repent, for the kingdom of heaven is at hand."
The personification of the hills in "Let the valleys rise to meet Him / And that hills bow down to greet Him" bears some resemblance to Philippians 2:10, specifically "at the name of Jesus every knee should bow," but I think that's just coincidental.