Because there are multiple languages across the world, it is easy for modern people to assume that language is a human invention. But no one invented it. It is actually a gift from God--the whole multiplicity of languages. God is the source. And, according to the Bible, God is the original speaker.
The first speech is God himself: "In the beginning was the Word, and the Word was with God, and the Word was God" (John 1:1). The Word is also known as the divine Son, who is Jesus Christ. God has also indicated that he created everything by speaking. "God said, 'Let there be light,' and there was light" (Gen. 1:3; see Ps. 33:6, 9). When he created mankind in Adam, he spoke to Adam (Gen. 1:28-30).
As a result, human language reflects divine language. In fact, it reflects God in his Trinitarian character. There is one God who is three persons, the Father, the Son, and the Holy Spirit. Because there is one God, language is a unified whole. But there is also a diversity of persons, resulting in a diversity of meanings in language.
Vern Poythress, Ph.D. is distinguished professor of New Testament, Biblical Interpretation, and Systematic Theology at Westminster Theological Seminary.
For Professor Poythress' full treatment of this question:
Vern S. Poythress, In the Beginning Was the Word: Language--A God-Centered Approach (Wheaton, IL: Crossway, 2009).