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.