Timothy Costelloe has been appointed the Archbishop-Designate until he is officially installed in the role in mid-March when he will become the city's sixth Archbishop.
Archbishop Hickey resigned when he turned 75 last year but has remained in the job until his replacement was announced.
Archbishop-designate Costelloe has previously spent time in Perth as a religious superior of the order of Salesians of Don Bosco.
He also worked as a parish priest and theology lecturer at the University of Notre Dame in Fremantle.
He says accepted the role with a sense of gratitude and humility.
"This is a big challenge. The holy father has asked me to do something that I hope I'm up to," he said.
"I'm certainly going to do my best, I'll commit all of my energy to this role."
Archbishop Hickey says the role requires tackling what he described as the increasingly difficult task of taking the Christian message to an increasingly secular society.
The Archbishop says it is vital the Catholic Church continues to hold onto its high moral and spiritual standards.
"That fight to preserve our standards, our vision of morality, our vision of human sexuality, is still a challenge, more a challenge now than it was when I started," he said.
Archbishop-designate Costelloe says he hopes to be a strong and positive voice for the church in Perth.
"From now on, this is my home, Perth is my home, Western Australia is my home," he said. "I look forward to becoming very much a part of the church here in Perth but of the wider society as well."