She was elected by the Church of Ireland as Bishop of Meath and Kildare, in the Republic of Ireland.
The married mother of two, who grew up in Belfast, said she was "excited and daunted" by the historic appointment.
The service of consecration took place at Christ Church Cathedral, Dublin.
In a sermon during the service, the Rev Nigel Parker from St Comgall's parish in Bangor, County Down, paid tribute to Mrs Storey.
He said: "It has been our privilege over the years to see you respond to our Father's love with love, trust and obedience.