Sheikhs Mahmood Kibaate, Habib Kabaasa are the 1st and 2nd deputy muftis.
Sheik Muzaata was also named the Public Relations Officer at Kibuli.
The group was elected Wednesday by the Council of Eminent Sheikhs (CES) at Kibuli Mosque.
Sheikh Ndirangwa replaces Sheikh Zubair Kayongo who passed away in April this year at Agha Khan Hospital in Tanzania.
His deputy, Sheikh Mahmood Kibaate, has been the acting Supreme Mufti for the last nine months.
Ndirangwa who has been serving as the District Kadhi of Kampala for almost five years thanked the council for electing him and calld for unity among Muslims.