Hanukkah is not described in the Hebrew Bible because the events behind the festival occurred after the period covered by the Old Testament historical books.
Daniel contains visions involving later kingdoms and the persecution of God's people. Many interpreters understand parts of Daniel 8 and 11 as referring to Antiochus IV Epiphanes and the crisis that led to the Maccabean revolt. These passages should be read as prophetic background rather than as instructions for celebrating Hanukkah.
The historical story itself is found most clearly in 1 Maccabees 1-4 and 2 Maccabees 6-10. These books describe the persecution, revolt and rededication of the Temple. They are not part of the Jewish Hebrew Bible. Their place in Christian Bibles varies among traditions.
John 10:22-23 provides the clearest New Testament reference. John identifies the occasion as the Feast of Dedication, notes that it was winter and places Jesus in the Temple courts in Jerusalem.
The passage confirms that the festival established after the Maccabean victory continued to be observed during the first century.