This question has already been answered before. You just have to read the Catholic Encyclopedia. Below, I have extracted out and rearranged parts from the encyclopedic entry in order to provide a concise answer for this question. I've also dug into some material that explains the reason for singing the Psalms, hymns, and spiritual canticles (Col 3:16): the reason is that Apostle Paul says so.
Colossians 3:16 (New International Version)
Let the message of Christ dwell among you richly as you teach and
admonish one another with all wisdom through psalms, hymns, and songs
from the Spirit, singing to God with gratitude in your hearts.
The History of the Offertory
The use of bread and wine is supported by St. Justin Martyr, an early Church Father, who said: "Then bread and a cup of water and wine are brought to the president of the brethren" (I Apol., lxv, cf, lxvii). The bread and wine alone were offerings to God by the laypeople, but soon they were accompanied by a silent prayer (presumed with certain to be the Offertory prayer, because originally the only Roman Offertory prayers were the Secrets and said silently) that God should accept these gifts, sanctify them, change them into the Body and Blood of his Son, and give Christians the grace of Communion in return. The Offertory was carried out during the Mass of the Faithful by the clergymen, while the laypeople in the congregation sang a psalm (the Offertory chant, or Offertorium), which was part of the Proper of the Mass. The Offertorium was once a whole psalm with an antiphon. By the time of the Gregorian Antiphonary, the psalm had been reduced to a few verses only, which caused much controversy and lamentation. Now, only the antiphon was sung, except at requiems. It's taken from the psalter, or other book of the Bible, or oftentimes, not a Biblical text. It refers in some way to the feast or occasion of the Mass, never to the offering of bread and wine. Only the requiem has preserved a longer offertory with one verse and the repetition of the last part of the antiphon (the text is not Biblical). In the Middle Ages, the public presentation of the gifts (bread and wine) by the people had disappeared. The medieval Offertory prayers varied considerably, and were established at Rome by the fourteenth century (Ordo Rom. XIV., 53, P.L. LXXVIII, 1165). The present Roman prayers were compiled from various sources, Gallican or Mozarabic. Since then, the prayers that modern-day Catholics may know form part of the Roman Mass.
According to this source, singing is the sign of the heart’s joy (Acts 2:46-47). Thus, St. Augustine says rightly, “Singing is for one who loves,” and there is also an ancient proverb: “Whoever sings well prays twice over.” Since the Offertory used to be a whole psalm and antiphon, it would make sense to sing or chant the Offertory, because singing is a way to express love for God and communication with God.
Acts 2:46-47 (New International Version)
Every day they continued to meet together in the temple courts. They
broke bread in their homes and ate together with glad and sincere
hearts, praising God and enjoying the favor of all the people. And the
Lord added to their number daily those who were being saved.