What is the biblical basis for believing in the Book of Mormon? I know that Mormons say the Bible and the Book of Mormon don't contradict. I don't know about that, but I would like to know whether there actually is a verse in the Bible that could support the belief in an exterior source such as the Book of Mormon, so highly regarded -by Mormons- as another revelation from God.
Cwallenpoole made it clear, that the Bible, as we have it today, is not complete. If one is not careful, it is easy to run into a negative evidence fallacy by supposing that simply because the Bible doesn't mention something, that something must be false. (That would be like saying "Jesus Christ" of the New Testament is false because that Name is never mentioned in the Old Testament.)

Before I also attempt to answer your question, let me prelude with a disclaimer: most members of the LDS church will hesitate to show "proof" or even "evidence" of the Book of Mormon's truthfulness, for the very existence of the Book itself is evidence of what is known as the Restoration, which is the fulfillment of prophecies concerning the dispensation of the fulness of times (the days before the Second Coming in which the Lord would send prophets to the earth again after a falling away first).

Mormons will remind anyone that the only way to truly believe in the Book of Mormon, or have a testimony of its truthfulness, is not by scholarly study, but by reading it and praying to ask God if it is true, and that an answer will come by the Holy Ghost.

So with that in mind, the following verses (in addition to those I've linked to) should be instructive. Keep in mind that while many people interpret these verses in many ways, this is one way the LDS population understands them:


Ezekiel 37:15-23 (The Stick of Judah and the Stick of Joseph. The Stick of Judah is written by Jews, in other words, is the Bible. The Stick of Joseph is the Book of Mormon, written by descendants of Joseph. More details about the sticks here.)
Isaiah 29:4,11-14 (A voice out of the dust. The Book of Mormon was buried for centuries until it came out of the ground and was translated. Because it is the same gospel that Christ teaches from the Bible, it is a familiar voice. Also, a vision of a sealed book taken to a learned man, and an unlearned man that could not read them. Plus the transcript of Joseph Smith's First Vision experience in 1820. These were fulfilled as recorded in JS-H 1:11-26,63-65.)
Ezekiel 17:22-23. (The highest branch of the high cedar is the royal family of Israel; the young twigs are the children, and the tender one is a man named Mulek, son of Zedekiah, who actually escaped and was led to the Americas. Lehi's group had already left Jerusalem, and later we learn that Mulek's group joined the Nephite nation.)
John 10:16. (Jesus refers to "other sheep" which would hear His voice. True, the gospel later did go to the Gentiles, but they heard the voice of His prophets and apostles, not His voice directly. These are the people of the Americas, and others. This is made clear in the Book of Mormon, where Jesus visited and ministered to them personally, established His Church on the American continent, and ordained prophets and disciples there, fulfilling all sorts of prophecies.)
Revelation 14:6-7. (An angel flying in the midst of heaven that had the everlasting gospel. This was Moroni, who buried the Book of Mormon, who later as a resurrected being, brought forth the Book of Mormon by Joseph Smith to go forth to all the earth.)
Amos 3:7. (Why would inhabitants of the American continent not have the gospel, if God loves all His children and wants them to know of His Son? So, God at least probably called prophets in America and they obviously prophesied. God's works are without end and His words never cease, so that God's canon of scripture is closed would not be logical, at best.)
Isaiah 5:26-27. (An ensign, or standard, would be lifted up to all nations to gather Israel before the Lord's coming.)


There are others. This list is not comprehensive, but I hope others will add to this as is proper.

The Bible and the Book of Mormon support each other. The Book of Mormon supports what the Bible says. All the prophets since the world began (including those in the Book of Mormon) knew there would be an apostasy of the Christian church in the New Testament and that God would set his hand a second time to recover His people. For example, see 2 Nephi, chapters: 27, 28, 29, 30, 31, 32, and 33, and Mormon 7:8-10 are a few, although the doctrine of Christ's mercy and Atonement is found all throughout the entire book.

Of particular interest is 1 Nephi 13 (especially the second half of the chapter) which discusses Nephi's vision of the settling of colonial America, the coming of Christians from Europe, and the introduction of the Bible ("which proceedeth forth from the mouth of a Jew") among the Native Americans, that it is holy and true, but that many plain and precious parts are actually missing.

So, I add these references to the Book of Mormon because they should help support the Bible references mentioned here that help to directly answer your question.

Finally, the notion of "infallibility" in scripture is misleading, because while God does inspire true scripture, imperfect but holy men write it down.

From the Title Page of the Book of Mormon (emphasis added):


  ... Which is to show unto the remnant of the house of Israel what great things the Lord hath done for their fathers; and that they may know the covenants of the Lord, that they are not cast off forever—And also to the convincing of the Jew and Gentile that Jesus is the Christ, the Eternal God, manifesting himself unto all nations—And now, if there are faults they are the mistakes of men; wherefore, condemn not the things of God, that ye may be found spotless at the judgment-seat of Christ.