His brother Dan said Nachman succumbed to cancer on Friday.
Nachman, known for his fiery personality and commanding media presence, helped establish Ariel in 1978.
Prime Minister Benjamin Netanyahu eulogized the mayor, saying Nachmann was "committed with every fiber of his soul to the revival of the Jews in their country and to building a flourishing city in Samaria."
Samaria is the biblical name for the part of the West Bank where Ariel is located. With 20,000 residents, it's one of Israel's largest settlements.
Palestinians see settlements as a hindrance to a two state solution as the communities are built on land they demand for their own state.