Joseph Fielding Smith
First came the carrying away of the ten tribes into Assyria, from which country they never to this day have returned. From these exiles many without question found their way into the area which formed the nations of northern Europe. . . . It was to be by scattering the children of Israel among the nations of the earth that the Lord would bless them and make them entitled to the blessings of the gospel. The Lord took measures for this scattering soon after the Israelites entered the land of Palestine and had received their inheritances. For a detailed account of this dispersion the reader is referred to the excellent work by Elder George Reynolds entitled, Are We of Israel? In this brief history the migrations and mixing of the Israelites in all parts of the earth is shown; therefore it is not needful here to go into any great detail showing this universal scattering. . . .
We who accept the Book of Mormon know that the Lord led the Nephites and the Mulekites out of Palestine to this western hemisphere. Likewise other colonies were taken to other parts of the earth. What became of the Ten Tribes we do not know, but from the prophetic utterances of the Nephite prophets we know that long before the coming of our Redeemer, the Israelites were scattered over the face of the globe. Nephi, writing of this scattering, had this to say:Wherefore, the things of which I have read are things pertaining to things both temporal and spiritual; for it appears that the house of Israel, sooner or later, will be scattered upon all the face of the earth, and also among all nations. And behold, there are many who are already lost from the knowledge of those who are at Jerusalem. Yea, the more part of all the tribes have been led away; and they are scattered to and fro upon the isles of the sea; and whither they are none of us knoweth, save that we know that they have been led away.  
Acts 17:24, 26
God that made the world and all things therein, seeing that he is Lord of heaven and earth, dwelleth not in temples made with hands;
And hath made of one blood all nations of men for to dwell on all the face of the earth, and hath determined the times before appointed, and the abounds of their habitation;
2 Nephi 29:12-13
For behold, I shall speak unto the Jews and they shall write it; and I shall also speak unto the Nephites and they shall write it; and I shall also speak unto the other tribes of the house of Israel, which I have led away, and they shall write it; and I shall also speak unto all nations of the earth and they shall write it.
And it shall come to pass that the Jews shall have the words of the Nephites, and the Nephites shall have the words of the Jews; and the Nephites and the Jews shall have the words of the lost tribes of Israel; and the lost tribes of Israel shall have the words of the Nephites and the Jews.
And it came to pass that the Lord of the vineyard went his way, and hid the natural branches of the tame olive tree in the nethermost parts of the vineyard, some in one and some in another, according to his will and pleasure.
And it shall come to pass in that day, that the Lord shall set his hand again the second time to recover the remnant of his people, which shall be left, from Assyria, and from Egypt, and from Pathros, and from Cush, and from Elam, and from Shinar, and from Hamath, and from the islands of the sea.
And he shall set up an ensign for the nations, and shall assemble the outcasts of Israel, and gather together the dispersed of Judah from the four corners of the earth.