Mr Trump made the announcement on Saturday morning after authorising new tariffs this week.
"There is literally nothing to be gained in the US.by imposing a tariff", Malcolm Turnbull said during a speech at the Financial Review Business Summit in Sydney.
In a post on his Twitter account, the United States president said he had spoken with the Australian prime minister.
President Trump has tweeted this morning that the USA is working very quickly on a security agreement so that it doesn't impose steel or aluminium tariffs on Australia.
Announcing the details of his tariffs in Washington yesterday, Mr Trump singled out Australia when he said he may exempt countries with which the USA has good trade and military relationships.
"Thank you for confirming new tariffs won't have to be imposed on Australian steel & aluminium - good for jobs in Australia and in USA!"
Turnbull's government reacted with shock last week when Trump announced that the US would be imposing stiff tariffs on imports of steel and aluminum.
Shadow trade minister Jason Clare welcomed the "great news" and congratulated the Coalition on securing the exemption which, he said, Australia deserved.
Major US trading partners have condemned Trump's decision to impose the punitive tariffs as protectionism and an affront to allies, amid growing fears of a global trade war.
Trade minister Steve Ciobo on Friday signed the 11-country deal, which will eliminate 98 per cent of tariffs in a marketplace worth close to $US14 trillion.
"While we hope that Australia will win exemptions from the latest steel and aluminium tariffs, this would be only a partial victory", Mr Willox said on Friday.
He said the threat of Australia sustaining collateral damage in a trade war also remained real.
"A positive relationship with Mr Trump and Mr Turnbull is now forged, and indirectly a close strategic and security relationship does help", Dr Dean said.
Mr Willox said the trade agreement will guarantee the free flow of data across borders for service suppliers and investors.
"History tells us they are bad, and they end up causing not just a contraction in the global trade but, as a result of that, a contraction in global growth", he told the ABC.