This article goes more into depth about the origins of The Jesus Prayer. I'll copy one section into this post, 4 ways this prayer is rooted in Scripture…
1) In its brevity and simplicity, it is the fulfillment of
Jesus' command that "in praying" we are "not to heap up empty phrases
as the heathen do;
for they think that they will be heard for their
many words. Do not be like them . . .(Matt. 6:7-8).
2) The Jesus
Prayer is rooted in the Name of the Lord. In the Scriptures, the power
and glory of God are present in
his Name. In the Old Testament to deliberately and
God's Name was to place oneself in his Presence.
Jesus, whose name in Hebrew means God saves, is the living Word
addressed to humanity. Jesus is the final
Name of God. Jesus is "the Name which is above all
other names" and it is written that "all beings should bend the knee at
the Name of Jesus" (Phil. 2:9-10). In this Name devils are cast out
prayers are answered (John 14:13 14) and the lame
are healed (Acts 3:6-7). The Name of Jesus is unbridled spiritual power.
3) The words of the Jesus Prayer are themselves based on
Scriptural texts: the cry of the blind
\ man \ sitting at the side of the road near
Jericho, "Jesus, Son of David, have mercy on me" (Luke 18:38); the ten
lepers who "called to him, 'Jesus, Master, take pity on us' " (Luke
17:13); and the cry for
mercy of the publican, "God, be merciful to me, a
sinner" (Luke 18:14).
4) It is a prayer in which the first step
of the spiritual journey is taken: the recognition of our own
sinfulness, our essential
estrangement from God and the people around us. The
Jesus Prayer is a prayer in which we admit our desperate need of a
Saviour. For "if we say we have no sin in us, we are deceiving ourselves
and refusing to admit the
truth" (I John 1:8).