The group's al-Nabaa newspaper identified Abu Musab al-Barnawi as the new "Wali" of its West Africa Province, a title previously used to describe long-time leader Abubakar Shekau.
The report did not say what Shekau's current status is.
The interview with al-Barnawi indicates a major change in strategy for the Nigerian extremists, who have attacked mosques with suicide bombers and gunmen, blown up suicide bombers in crowded marketplaces and killed and kidnapped school children.
The targeting of students accounts for its nickname Boko Haram, which means Western education is sinful or forbidden.
Wednesday's announcement indicates a coup by Boko Haram breakaway group Ansaru against Shekau, and follows a trend of extremist Islamic groups moving away from al-Qaida to the Isis, analyst Jacob Zenn said.
Ansaru broke away from Boko Haram because it disagrees with the indiscriminate killing of civilians, especially Muslims. Al-Barnawi is the pseudonym of a Nigerian journalist allied with Ansaru, which is known for kidnapping foreigners, according to Zenn.