Angel of Brit

The prophet Elijah  is known as "the angel of brit." Indeed, the mohel  uses that title as he summons Eliyahu to stand at his right during the brit. Elijah has an additional task, hopefully to be fulfilled speedily in our days: to be the harbinger of the arrival of Messiah, as we read in the penultimate verse of the Prophets:

Behold, I send you the prophet Eliya before the arrival of the great and awesome day of God .                       Malachi 3:23

The two "jobs" of Elijah are related.

Elijah is also known to us by his original name:

Rabbi Shimon ben Lakish says: Elijah is Phinehas.                          Midrash Yelamdenu.

In the third verse of Parashat Pinḥas [Numbers 25:12], we read that Phinehas was rewarded for his act of zealotry with the "covenant of peace" (brit shalom).

Malbim explains that "shalom" essentially is harmony. Shalom is related to life [Malachi 2:5]. Indeed, Phinehas lived a long life. The verse [Judges 20:28] tells us that Phinehas was still alive at the time of the matter of the concubine of Gibeah generations after the Tribes of Israel entered the Land. Certainly, according to the rabbinic tradition that Elijah is Phinehas, he lived an exceptionally long life. Bodies are composed of disparate parts. When there is a lack of harmony among the parts, death results. "Shalom," peace, is the situation of internal harmony which prolongs life.

With Malbim's insight, we can understand Elijah's two roles. Messiah will usher in the era of harmony. Thus, Elijah/ Phinehas’ blessing of "shalom" qualifies him (or perhaps obligates him) to be the one who will announce the arrival of Messiah.

As far as Brit Mila is concerned, it is essentially the God-given opportunity to act upon our own bodies to achieve harmony between our physical and spiritual components. As such, brit is another application of "shalom", and hence the purview of Elijah.