Translation:Arukh ha-Shulchan/Orach Chaim/683
On Hanukkah, we do the complete Hallel prayer, because every day a miracle occurred through that one jug of oil. And furthermore: Since every day the candles differ (one is added each night) when following the practice of Mehadrin min Hamehadrin, it becomes like Sukkot, where the offerings differed each day and the complete Hallel is therefore recited. And there is another reason: because we read the Torah portion relating to leaders of the tribes (Naseim) [specifically their offerings at the inauguration of the Mishkan]on Hanukkah, and there each day's Nasi differed as well, and would have had to say the complete Hallel over his offering.(Beit Yosef)
Furthermore: As I have written in Siman 670, the eight days of Hanukkah were enacted in place of the days of eight days of Sukkot, which could not be observed at that time. Therefore the complete Hallel is said as it would be on Sukkot.
On all eight days of Hanukkah, we do not say Tachanun, צדוק הדין ,צדקתך צדק, יענך -(the prayer that one says when entering the cemetery). This also applies to the afternoon prayer on the eve of Hanukkah, where we do not say Tachanun, like I have written in chapter 131. These days are also times where it is forbidden to fast, like I have written in chapter 670. On Chanukkah some arrange special festive meals, including in them the singing of songs of praise and gratitude, as I have written there.