Why will we merit the ingathering of the exiles in merit of our study of Mishnah? 

The Midrash teaches, "All these exiles will be gathered in only by virtue of the study of Mishnayos."

Why specifically Mishnayos?

The Second Beis HaMikdash was destroyed because of undeserved hatred, while the First Beis HaMikdash was destroyed “because [the people of that generation] did not pronounce a blessing before they began their study of the Torah,” i.e., because they did not hold the Torah in due esteem. The study of Mishnayos helps to right both these wrongs.

The Mishnah deals with practical halachic rulings which have to be understood, yet all sides acknowledge the truth of what it states, without dissent. By all agreeing to one ruling, even though they are men of varied understanding, students of the Mishnah demonstrate that it is G-d Who gave us His Torah – one Torah, for Israel, who are one people.

Studying the scriptures does not have this quality.  There is no particular opportunity for disagreement, as the study is not directed towards determining practical legal decisions.  There is also no need to be frequently reminded of the Giver of the Torah by reciting a blessing, because one is frequently reminded by the text itself:  “And G-d said...,” “And G-d spoke...,” and the like.

As far as the study of Gemara is concerned, every individual argues out the reasoning implicit in the Mishnah and articulates his own stand, according to the depth of his understanding. The underlying unity here between the various conflicting scholars is not readily observable.

Only the study of Mishnah combines both qualities:  It emphasizes the unity among all scholars, and this reminds us of G-d Who gave us the Torah to unite us into one people.

(Sources: Vayikra Rabba 7:3.  Yoma 9b. Nedarim 81a. Sanhedrin 33a.  Teshuvot U’Biurim of the Rebbe, sec. 4)