"This is the best possible set of arrangements and really sets the standard in where free trade should be," Treasurer Scott Morrison said in Sydney on Friday.
"We believe, as we have always said, it is a great outcome for the US and for Australia."
Australian delegations, headed by Prime Minister Malcolm Turnbull and Foreign Affairs Minister Julie Bishop, have aggressively lobbied the White House in recent months to secure the exemption.
The US will place quotas or volume limits on steel and aluminium from Australia and Argentina.
"The US has agreed on a range of measures with Argentina and Australia, including reducing excess aluminium production and excess aluminium capacity, measures that will contribute to increased capacity utilisation in the United States, and measures to prevent the trans-shipment of aluminium articles and avoid import surges," Mr Trump wrote in a proclamation on Thursday.
Australia had previously received a temporary reprieve from the tariffs.
The White House announced negotiations with Mexico, Canada and the EU did not go so well and from Friday, the US would slap the three allies with steel and aluminium tariffs.
All three quickly responded with threats of tariffs on US goods.
"This is a bad day for world trade," head of the EU bloc's executive Jean-Claude Juncker said in Brussels.
Manfred Weber, an ally of German Chancellor Angela Merkel, said "we will have no choice but to defend European industry, jobs and interests".
Mexico announced it will retaliate with duties on US products including fruit, pork bellies, cheese and flat steel.
Canada is preparing "a whole series of options" to retaliate, a Canadian official told the Toronto Star.