Jacob intimated why he considered Ephraim and Manasseh his own sons by referring to them as “your two sons who were born to you in Egypt before I came to you.” Even though Ephraim and Manasseh were born and raised in Egypt before Jacob’s arrival, they grew up true to their grandfather’s ideals. Therefore, Jacob considered them as loyal to him and his ideals as his own children.1
When Jacob sensed that he was about to die, he sent for Joseph. Jacob instructed Joseph not to bury him in Egypt, fearing that the Egyptians might turn his grave into an object of worship since it was his blessing that had ended the years of famine. Instead, Jacob instructed Joseph to bury him in the family tomb in Hebron. Some time later, when Jacob became ill, Joseph took his two sons, Manasseh and Ephraim, to Jacob in order for them to receive his final blessing. Jacob surprised Joseph by informing him that he was making Joseph’s sons the heads of two separate tribes, on an equal footing with Jacob’s own sons.
The Reward of Loyalty
וַיֹּאמֶר . . . אֶל יוֹסֵף רְאֹה פָנֶיךָ לֹא פִלָּלְתִּי וְהִנֵּה הֶרְאָה אֹתִי אֱלֹקִים גַּם אֶת זַרְעֶךָ:
(בראשית מח:יא)
[Jacob] said to Joseph, “I dared not even hope to see your face, yet now G‑d has even shown me your children.”
Genesis 48:11
Footnotes
1.
Likutei
Sichot, vol. 15, p. 435.


I feel there is some source of additional data beyond the Torah I am missing. When I read the assigned verses I do not see the interpretation that the Rebbe is drawing.
The assigned verse appears to be incorrect. The correct verse is Genesis 48:5: "And now your two children that were born in Egypt before I arrived to you". The Rebbe is explaining why Jacob has to emphasize "that were born in Egypt before I arrived". The verse could have cut those words out and just said "your two children will be like Reuven and Shimon".
The Rebbe explains that the reason that Ephraim and Menashe were accepted as two tribes is because they grew up in Egypt, far away from the influence of Jacob. The fact that they were able to grow up in their grandfather's ways while never meeting him and living in a hostile environment shows that they complete him. They are the fulfillment of the power of Jacob. They are able to bring the holiness of Jacob into the rest of the world. Therefore, they become tribes.
Thanks for the follow-up. So often when reading Scripture I go over verses thinking I understand what is being communicated only to discover later that I missed a salient point due to my lack of understanding of the environment in which the verses were written.