Sources

Esau & Jacob fighting in the womb and the Prophecy:  Genesis 25:19-23.
They will not rule concurrently:  Talmud Megila 6a.
Esau will dominate This World and Jacob the Next World:  Midrash Yalkut Shimoni 110.
Jacob = Will Overtake:  Midrash Pirkei DeR' Eliezer 32
Esau forsakes his birthright:  Genesis 25:29-34
Jacob snatches the blessings:  Genesis 27.
Preparing for battle:  Genesis 32:4-33:16.
Esau's first royal dynasty:  Genesis 36:31-39
Jacob's first royal dynasty overtaking Esau's:  Midrash Bereshit Rabba 83:2.
Magdiel rises to greatness... Rome:  Midrash Pirkei DeR' Eliezer 38. The meaning of his name "Magdiel" which contains allusions to the words "Magdil = increase/make big" and "E-l = G-d" meaning G-d has taken this tribe to greatness. This is the same meaning of "Rome" = high. (Gur Aryeh on Genesis 36:43). Also see the Radak's (Rabbi David Kinchi) commentary on Obadiah (in the beginning): "The early Romans were mostly from Edom (Esau)".

Rome = Western World:  As alluded to in Daniel's prophecy regarding "The King of the North": "he will exalt himself and magnify himself over every powerful one" (11:36) meaning that Rome will spread across the whole world like no other kingdom has (Ramban on Genesis 36:43).  It's interesting to note that there was one more chief after Magdiel: Iram (עירם). This name obviously shares more direct resemblance to "Rome". Indeed, the Midrash (Rabba, Vayishlach 83:4) writes he is called by that name for he will amass (Arema / ערימה) treasures for Moshiach. That is, its greatness will be used to support Jacob/Moshiach (Sefer Hasichot 5751 Pt.1 p.172).
Deliverers (will ascend up the Mount of Esau):  Obadiah 1:25. "Deliverers" in the plural alludes to Moshiach and his ministers (Metzodat David)
Moshiach being compelling:  "... And all the nations will flow to it [Jerusalem]... and they shall say, "Come, let us go up to the L-rd's mount, to the house of the G-d of Jacob, and let Him teach us of His ways, and we will go in His paths..." (Isaiah 2:2-3).  Note even though the nations are going up, they are "flowing" like water that gravitates down, as they'll be so attracted to Moshiach (MALBI"M's (Meir Leibush ben Yehiel Michel Wisser) commentary on this verse).