he was appointed coadjutor bishop of shrewsbury and titular bishop of miletopolis on 18 december 1931. his consecration to the episcopate took place on 28 january 1932, the principal consecrator was thomas leighton williams, archbishop of birmingham, and the principal co-consecrators were john patrick barrett, bishop of plymouth and hugh singleton, bishop of shrewsbury. moriaty succeeded as the bishop of shrewsbury on 17 december 1934. he was made assistant to the pontifical throne in 1944, the year of his golden jubilee in priesthood, when he was presented with a cheque for £3,450 from the clergy and laity of his diocese, which he donated for the funding of training priests from the diocese at the english college.