In chapter 10, Kṛṣṇa lists the best of everything and says that is him. Among sages, he names Vyāsa. Tradition says Vyāsa composed the Mahābhārata, so the author is a line inside his own book.
Going deeper
10.37 is a verse of four pairs: of the Vṛṣṇis, Kṛṣṇa is Vāsudeva; of the Pāṇḍavas, Arjuna; of sages, Vyāsa; and of seers, Uśanā, called Śukra. The verse before, 10.36, gives gambling among the fraudulent, the brilliance of the brilliant, victory and effort. The verse after, 10.38, names the principle of punishment, policy, silence among secrets and wisdom among the wise. Vyāsa is also named at 10.13, among the seers who declare this of Kṛṣṇa, and at 18.75, where Sañjaya credits Vyāsa's grace for what he heard. Tradition, the story says, holds that Vyāsa composed the Mahābhārata, so the author appears as one line inside his own book. The Gītā itself only places his name in Kṛṣṇa's list. See chapter 10 and what the Gītā says about devotion.