DUBLIN — The Roman Catholic Church’s much-criticized leader in Ireland ­an­nounced Friday that the Vatican has approved his successor, a reform-minded priest who has been outspoken on the need for more church accountability on child sex abuse.

Cardinal Sean Brady, who resisted calls to resign in 2010 despite being implicated in covering up abuse of children, named Monsignor Eamon ­Martin as his eventual successor at a press conference on the front steps of St. Patrick’s ­Cathedral in Armagh, the ecclesiastical capital of Ireland.