The two bodies revealed they have agreed two Memoranda of Understanding to ensure there is continuity once the UK leaves the European Union.
The MoUs cover trade repositories and alternative investment funds (AIFs).
These agreements will provide reassurance by ensuring arrangements are in place for cross-border cooperation between the FCA and ASIC.
The FCA and ASIC say they also support the continuity of existing equivalence decisions to provide certainty to businesses post-Brexit.
Andrew Bailey, chief executive, FCA said: “The FCA and ASIC have always had a strong relationship, which will continue after Brexit.
“The MoUs we have agreed today will ensure the FCA and ASIC have uninterrupted exchange of information and can supervise cross-border activity of firms.
“They provide a strong signal to the markets that the UK will continue to play an important role after Brexit.
“The MoUs will also provide much-needed assurance to our regulated stakeholders.
“We also support the continuity of existing equivalence decisions which will minimise disruption for firms in the UK and Australia.”
James Shipton, Chair, ASIC said: “ASIC is pleased to have cooperation arrangements in place with the FCA on trade repositories and alternative investment funds.
“While the FCA and ASIC have always maintained a very close relationship on supervisory and enforcement matters, these two MOUs will enhance cooperation and information sharing between the authorities.
“Our commitment to ensuring the continuity of equivalence decisions will provide certainty to businesses and consumers and contribute to a fair, strong and efficient financial system.”
These MoUs will enter into force on the date EU legislation ceases to have direct effect in the UK.
This will occur when the UK leaves the EU, or at the end of the transition period if a Withdrawal Agreement is in place.