Mullally will succeed Richard Chartres to become the 133rd person to hold the role which falls below only the Archbishop of Canterbury and the Archbishop of York in the church's hierarchy.
"It is a great honour to be nominated," Mullally, 55, who is married with two children, said in a statement. "Having lived and worked in London for over 32 years, the thought of returning here is about returning home."
She will be formally installed as the bishop at London's St Paul's Cathedral in the new year.
Mullally was the former Chief Nursing Officer for England, the youngest person to be appointed to that post, before she was ordained in 2001. She became Bishop of Crediton in southwest England in 2015.
At attempt to bring in women bishops failed in 2012 when traditionalist lay members defeated the move in a vote in the General Synod, the Church's governing body. New proposals which gained wider acceptance were approved the following year.
The worldwide Anglican community remains deeply split over the issue of women clergy. Women serve as bishops in the United States, Canada, Australia and New Zealand, but Anglican churches in some developing countries, particularly in Africa, still do not ordain women as priests.
(This story has not been edited by NDTV staff and is auto-generated from a syndicated feed.)
Get Breaking news, live coverage, and Latest News from India and around the world on NDTV.com. Catch all the Live TV action on NDTV 24x7 and NDTV India. Like us on Facebook or follow us on Twitter and Instagram for latest news and live news updates.