The 54 year old one time corporate lawyer has been installed as Archbishop during a ceremony at Saint Mary's Cathedral in Sydney.
He takes over from Cardinal George Pell who left the position in February to become the Vatican's finance chief in Rome.
Archbishop Fisher said he wants to use the role to reach out to those who have felt alienated from the Catholic Church, including gay people and the divorced.
"I think the Catholic Church is and should be a church for the whole of humanity," he said.
"Our arms are wide open for everyone. So whatever the struggles in their life, whether that's with their sexuality or their marital history or any other issues, I want to say to them: 'Come to the Church. The Church loves you because God loves you’."
Archbishop Fisher said he had been moved by recent calls from Pope Francis for the Catholic Church to adopt a greater openness towards gay people and divorced Catholics who have remarried.
"I have a consciousness now of the struggles of people with same sex attraction", he said.
"Our concern should be there to help them rather than to be adding to their problems and I fully back the view that we should be compassionate to people with a same sex attraction or with other struggles in their life."
The new archbishop said he also wanted to use his new role to reach out to younger Catholics and to restore public trust tarnished in the wake of recent paedophile scandals involving Catholic priests.
"We have to be very honest with ourselves and with everybody else about what has gone wrong", he said.
"We need to own up to that and show that we are genuinely ashamed and contrite and determined that that will never happen again," he added.
"We have to make sure that the victims are given every help they can be to be healed of what's been done to them and I think we have to put in processes for the future that mean that paedophiles can't be in positions like this again and that when there are complaints, they are dealt with very quickly."
Archbishop Fisher said he holds strong views on a number of social issues, particularly the treatment of asylum seekers.
"There is no doubt that we have to do what we can in this country to make sure that people smugglers have no incentive to continue that deadly practice", he said.
"But that said, we don't want to have such strong disincentives that we end up being unjust, especially to children", he added.
"I think all people of good will in this country would be deeply uncomfortable with the thought of having people incarcerated in horrible camps and who go on to suffer further psychological damage".
