The Old Testament reading for the Second Sunday in Advent (Malachi 4:1–6) serves as a standard source for the orienting of the pastor and the people toward the East in worship. It instructs us to face the direction of expectant waiting for our Lord, the Sun of Righteousness, who will come as the dawn from the East. When we orient ourselves in this way, the eschatological expectation of the Christ who once came by the virgin for the cross, who now comes in the Sacrament of His Body and Blood, and who will indeed come again in glory is incorporated into every Sunday. So just as we see every Sunday as a remembrance of or a ‘mini’ Christmas, Maundy Thursday, Good Friday, and Easter Sunday, so also we should see every Sunday as a remembrance of that eschatological reality. And as an aid for doing this, pastors and people use their bodies to help form the thoughts of their minds and the feelings of their hearts. For worship is not just in the mind or the heart, but the whole person—body and soul, heart and mind—for this Jesus says, is the first and greatest commandment (Luke 10:27). Thus we orient ourselves—whether this is the case geographically or not—toward God in prayer and even in the Sacrament in expectation of His promised return. Here is a snippet from St. John of Damascus on this very thing.

It is not without reason or by chance that we worship towards the east. But seeing that we are composed of a visible and an invisible nature, of a nature partly of spirit and partly of sense, we render also a twofold worship to the Creator; just as we sing both with our spirit and with our bodily lips, and are baptized with both water and Spirit, and are united with the Lord in a twofold manner, being sharers in the mysteries and in the grace of the Spirit. Since, therefore, God is spiritual light, and Christ is called in the Scriptures ‘Sun of righteousness’ [Mal 4:2] and ‘Dayspring [Zech 3:8, 6:12 LXX; Lk 1:78], the east is the direction that must be assigned to his worship. For everything good must be assigned to him form whom every good thing arises. Indeed the divine David also says, ‘Sing to God, O kingdoms of the earth; sing praises to the Lord, to him who rides upon the heaven of heavens towards the east’ [Ps 67:33–34 LXX]. Moreover the Scripture also says, ‘And God planted a garden in Eden, in the east; and there he put the man whom he had formed’ [Gen 2:8]; and when he had transgressed his command he expelled him and made him to dwell over against the delights of Paradise, which clearly is the west. So, then, we worship God seeking and striving after our old fatherland. . . . Moreover Christ, when he hung on the Cross, had his face turned towards the west, and so we worship, striving after him. And when he was received again into heaven he was borne towards the east, and thus his apostles worship him, and thus he will come again in the way in which they beheld his going towards heaven; as the Lord himself said, ‘As the lightning comes from the east and shines as far as the west, so will be the coming of the Son of Man’ [Mt 24:27]. So, then, in expectation of his coming we worship towards the east. But this tradition of the apostles is unwritten. For much that has been handed down to us by tradition is unwritten.

St. John of Damscus, Expositio fidei, 85.

And here’s another from the angelic doctor, St. Thomas Aquinas:

To adore facing east is fitting, first, because the movement of the heavens which manifest the divine majesty is from the east. Secondly, paradise was situated in the east according to the Septuagint version of Genesis, and we seek to return to paradise. Thirdly, because Christ, who is the light of the world is called the Orient, who mounteth above the heaven of heaven to the east, and is expected to come from the east according to Matthew, as lightning comes of the east, and shines even to the west, so also will the coming of the Son of Man be. 

St. Thomas Aquinas, S. Th. II-II, 1. 84, a. 3 ad 3.

Fr. Charles McClean has a fine essay in three parts on this topic in the Gottesdienst print journal Volume 20 (2012), Numbers 2 (Trinity), 3 (Michaelmas), and 4 (Christmas). You may purchase these individually in PDF format HERE.