Securing an agreement with the country is a top priority for the UK but the Australian government has sent out mixed messages in recent days.
Prime Minister Malcolm Turnbull promised an “early... very strong, very open” agreement with Britain after meeting Theresa May last weekend.
But trade minister Steven Ciobo has described his country’s historical tie with the UK as “a relationship of yesteryear” and dampened hopes of a swift deal, insisting formal negotiations could not begin until the UK had finally left the EU.
Mr Johnson will meet counterpart Julie Bishop at the annual Australia-UK Ministerial Meeting in London.
The Foreign Secretary said: “Australia is a long-standing and true friend of the UK, and I look forward to productive talks on how we tackle some of the challenges facing both of our great nations.
“This is a fantastic opportunity to reaffirm how important the UK-Australia relationship is to us and to celebrate our shared history, values and the strong links between our people.”
The meeting, which is being held at the Royal Hospital in Chelsea, home to veteran soldiers, also includes talks between Defence Secretary Sir Michael Fallon and opposite number Marise Payne.
They will focus on the terror threat, including tackling Islamic State, also known as Daesh, and the humanitarian crisis in Syria.
Sir Michael said: “Britain and Australia have a rich history of close military partnership and our defence alliance is as strong as ever. From vital intelligence sharing to the fight against Daesh, we’re working together to keep our people safe.”