This truth is taught plainly in the Book of Mormon.
King Benjamin taught it:
6 I say unto you, if ye have come to a knowledge of the goodness of God, and his matchless power, and his wisdom, and his patience, and his long-suffering towards the children of men; and also, the atonement which has been prepared from the foundation of the world, that thereby salvation might come to him that should put his trust in the Lord, and should be diligent in keeping his commandments, and continue in the faith even unto the end of his life, I mean the life of the mortal body—
7 I say, that this is the man who receiveth salvation, through the atonement which was prepared from the foundation of the world for all mankind, which ever were since the fall of Adam, or who are, or who ever shall be, even unto the end of the world. (Mosiah 4)
Alma-1 referenced it in his baptismal prayer:
13 And when he had said these words, the Spirit of the Lord was upon him, and he said: Helam, I baptize thee, having authority from the Almighty God, as a testimony that ye have entered into a covenant to serve him until you are dead as to the mortal body; and may the Spirit of the Lord be poured out upon you; and may he grant unto you eternal life, through the redemption of Christ, whom he has prepared from the foundation of the world. (Mosiah 18)
Alma-2 taught it:
25 Now, if it had not been for the plan of redemption, which was laid from the foundation of the world, there could have been no resurrection of the dead; but there was a plan of redemption laid, which shall bring to pass the resurrection of the dead, of which has been spoken.
...
30 And they began from that time forth to call on his name; therefore God conversed with men, and made known unto them the plan of redemption, which had been prepared from the foundation of the world; and this he made known unto them according to their faith and repentance and their holy works. (Alma 12)
There are other examples, too.
In the Book of Enoch, we get a description of Enoch's vision of "the Son of Man" being prepared before the foundation of the world to be "a fountain of righteousness" and "the light of nations."
1. In that place I beheld a fountain of righteousness, which never failed, encircled by many springs of wisdom. Of these all the thirsty drank, and were filled with wisdom, having their habitation with the righteous, the elect, and the holy.
2. In that hour was this Son of man invoked before the Lord of spirits, and his name in the presence of the Ancient of days.
3. Before the sun and the signs were created, before the stars of heaven were formed, his name was invoked in the presence of the Lord of spirits. A support shall he be for the righteous and the holy to lean upon, without falling; and he shall be the light of nations.
4. He shall be the hope of those whose hearts are troubled. All, who dwell on earth, shall fall down and worship before him; shall bless and glorify him, and sing praises to the name of the Lord of spirits.
5. Therefore the Elect and the Concealed One existed in his presence, before the world was created, and for ever. (1 Enoch 48)
Here we have yet another connection between the Book of Enoch and the Book of Mormon, supporting the idea that some version of this text was present on the Brass Plates, and that the priesthood tradition of the Nephites more closely followed the High Priest/prophetic tradition than the Deuteronomic tradition we find in the Old Testament.