Assange continues to face espionage charges in the United States and remains in London's Belmarsh prison, held there since 2019 while fighting extradition proceedings.
It is the first time since November, 2019, that he has accepted a consular visit and the first time a high commissioner has met with the Australian behind bars.
Mr Smith told the ABC on his way into the prison on Tuesday that it was "very important that the Australian government is able to discharge its consular obligations".
"I'm very keen just to have a conversation with him, check on his health and wellbeing and hopefully see whether regular visits might be a feature of the relationship with Mr Assange going forward," the high commissioner said.
Assange is keen to obtain diplomatic support from Australia in his battle to avoid extradition to the US and to be freed from jail.
After his visit Mr Smith would not comment on whether that issue had been discussed with Assange.Â
"In accordance with usual consular practice, and as agreed with Mr Assange, I do not propose to comment on any details of our meeting," he said in a statement.
Appeals to stop Assange from being extradited to the US are still before the UK courts.
On the weekend Assange's father John Shipton welcomed news that Mr Smith would visit his son.
"It will provide an opportunity for the high commissioner to see the appalling conditions Julian is kept in and the terrible toll that his ongoing incarceration is having on his health and on his family," he said in a statement on Saturday.
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