The UK is expected to offer Australia a trade deal later on Friday, under which both countries would phase out taxes on imports over 15 years.
The cabinet was reportedly split on what terms to propose, amid concerns UK beef and lamb farmers could be undercut by larger Australian producers.
But the dispute was apparently resolved after Boris Johnson pushed for unity.
International Trade Secretary Liz Truss will formally make the UK offer to her Australian counterpart later on Friday.
If accepted, it would also lead to quotas - limits - on tax-free trade between the two countries to be phased out.
The National Farmers' Union (NFU) has warned that freeing up the UK-Australian meat will lead to hundreds of British cow and sheep breeders going out of business.
Ministers are keen to strike as many trade deals as possible following Brexit, and Ms Truss wants one in place with Australia by the time the UK hosts the G7 summit - of leading economies - in June.
But she had reportedly been at odds with Environment Secretary George Eustice over the possible impact on farmers of removing tariffs - import duties.
With these differences seemingly resolved at a Downing Street meeting chaired by the prime minister on Thursday, Ms Truss will put the UK's terms for a deal to Australian counterpart Dan Tehan when they hold an online meeting later on Friday.
Speaking on a visit to Portsmouth, Mr Johnson said: "We are certainly looking at doing free trade deals around the world.
"They present a fantastic opportunity for our farmers, for businesses of all kinds, for our manufacturers. We should see these new openings not as threats but as opportunities."
Mr Tehan said he was "confident" of reaching an agreement with the UK by early June, having had "very positive discussions" with Ms Truss, the news.com.au website. reported.
