“It is related that when Julian had received the wound, he filled his hand with blood, flung it into the air and cried, "Thou hast won, O Galilean."”

Ecclesiastical History, Book III, Ch. 20 (c. 429); this is usually accepted as the origin of the spurious tradition of the last words of Julian being "Thou hast won, O Galilean." No mention of such a declaration occurs in the accounts of any earlier writers, even those most hostile to Julian.
Context: Julian’s folly was yet more clearly manifested by his death. He crossed the river that separates the Roman Empire from the Persian, brought over his army, and then forthwith burnt his boats, so making his men fight not in willing but in forced obedience. The best generals are wont to fill their troops with enthusiasm, and, if they see them growing discouraged, to cheer them and raise their hopes; but Julian by burning the bridge of retreat cut off all good hope. A further proof of his incompetence was his failure to fulfil the duty of foraging in all directions and providing his troops with supplies. Julian had neither ordered supplies to be brought from Rome, nor did he make any bountiful provision by ravaging the enemy’s country. He left the inhabited world behind him, and persisted in marching through the wilderness. His soldiers had not enough to eat and drink; they were without guides; they were marching astray in a desert land. Thus they saw the folly of their most wise emperor. In the midst of their murmuring and grumbling they suddenly found him who had struggled in mad rage against his Maker wounded to death. Ares who raises the war-din had never come to help him as he promised; Loxias had given lying divination; he who glads him in the thunderbolts had hurled no bolt on the man who dealt the fatal blow; the boasting of his threats was dashed to the ground. The name of the man who dealt that righteous stroke no one knows to this day. Some say that he was wounded by an invisible being, others by one of the Nomads who were called Ishmaelites; others by a trooper who could not endure the pains of famine in the wilderness. But whether it were man or angel who plied the steel, without doubt the doer of the deed was the minister of the will of God. It is related that when Julian had received the wound, he filled his hand with blood, flung it into the air and cried, "Thou hast won, O Galilean." Thus he gave utterance at once to a confession of the victory and to a blasphemy. So infatuated was he.