The current Bishop of Kaduna will take on the role, working closely with the Archbishop of Canterbury, which reaches out to Anglican churches across the world.
He was said to be selected out of an initial field of applicants from Oceania, Asia, Africa, Europe and the Americas.
When advertised the Church said it was looking for someone to "assist the Communion to become even more faithful to, and engaged in, God's mission of reconciliation".
Speaking about the appointment, Archbishop of Canterbury Justin Welby said: "I warmly welcome the appointment of Bishop Josiah and look forward to working closely with him in the renewal of the Anglican Communion amidst the global challenges facing us today."
Dr Idowu-Fearon has served in his role in Nigeria since 1998 and is seen as an expert in Christian-Muslim relations.
Speaking about his new challenge, he said: "I am excited to take up the post of Secretary General of the Anglican Communion, and to continue the fine work undertaken by my predecessors in this office.
"It is a privilege to be so honoured and recognised by the Communion for this leadership position. I look forward to serving the Anglican family with my future colleagues at the Anglican Communion Office and the Office of the Archbishop of Canterbury."
Bishop Josiah, who is married to Comfort and has two children, Ibrahim and Ninma, is expected to take up the role in July 2015.