The Catholic Church believes the use of blessed water goes back to the Apostles and in particular to the Apostle Matthias, the replacement Apostle for Judas Iscariot. The earliest written documentation of Holy Water by Christians is in the 300s AD in the Apostolic Constitutions, which was thought to be written by St Clement of Rome. Here's the portion from the Constitutions:
XXIX. Concerning the water and the oil, I Matthias make a constitution. Let the bishop bless the water, or the oil. But if he be not there, let the presbyter bless it, the deacon standing by. But if the bishop be present, let the presbyter and deacon stand by, and let him say thus: O Lord of hosts, the God of powers, the creator of the waters, and the supplier of oil, who art compassionate, and a lover of mankind, who hast given water for drink and for cleansing, and oil to give man a cheerful and joyful countenance; do Thou now also sanctify this water and this oil through Thy Christ, in the name of him or her that has offered them, and grant them a power to restore health, to drive away diseases, to banish demons, and to disperse all snares through Christ our hope, with whom glory, honour, and worship be to Thee, and to the Holy Ghost, for ever. Amen.