Omniscience is a characteristic of the Christian God from Antiquity, and it is discussed in many patristic texts.

The association of rationality as God is likewise just as old, and rationality is paired with discussions of omniscience in Christian theological tracts on theodicy from late Antiquity and the Middle Ages. However, it's not quite right (theologically speaking) to say that rationality is an attribute of God, particularly in medieval contexts. Rather, the part of a human which wants to be in accord with God is called the "rational". To quote Hugh of St. Victor (d.1143):

Propter voluntatem rationis, quae voluntati divinae per obedientiam subiiciebatur, dixit: Spiritus quidem promptus est

Because of the Reason, which was subjected to the will of the divine through obedience, Christ said: "The spirit is indeed willing."¹

This subordination occurs because:

Secundum voluntatem rationis, iustitiae consensit, et iustitiam approbavit

Following his Reason, he agreed to righteousness and approved the rightness.²

That is, the righteousness of God and the rightness of His purpose.

In other words, according to medieval theologians, what we call 'reason' is accord with the divine. God cannot really be said to possess it; it is nonsensical and tautological to say that God is in accord with God.

I would be interested to see if this theological understanding changes later.

¹ Patrologia Latina 176.0841D ² PL 176.0842C