The deal was agreed in principle earlier this year and will see many tariffs removed between the UK and Australia.
But the legal text is yet to be hammered out.
Ms Truss said that lawyers will have finalised a text sometime this year.
“We’re going through the same process that we went through with Japan ” she told MPs on the International Trade Committee.
“You reach an agreement in principle which is really addressing a lot of the knotty issues and showing the deal can be done, but then there is further work to translate that into legal text.”
“We need to get the text right.
“I am not going to give a commitment of a definite date.
“But we are hoping to complete that towards the end of this year.”
The deal will remove £124 million in tariffs paid by UK exporters each year, and £34 million for Australian exporters, Ms Truss said.
However it has been criticised by many British farmers who are worried about being undercut by food, especially meat, from Australia.
MPs also raised questions about how environmentally friendly it is to ship food to and from the other side of the world.
Ms Truss argued that producing some products in Australia and New Zealand is more climate friendly, and that emissions from shipping are low.
“In many cases it can be more environmentally friendly trading these products than producing them locally,” she said.
“You have to take it on a case-by-case basis.
“But the logic of your argument is that you wouldn’t trade with anybody, even across the UK and we would all just eat food from our local village.”
By selling pigs trotters to China the UK can reduce wasted food that British shoppers do not want to eat, she said.
