The anthem will no longer refer to Australia as "young and free" - in an attempt to reflect the country's long indigenous history.
The announcement was a surprise but welcomed across the government.
Mr Morrison said he hopes the change will create a "spirit of unity".
People inhabited Australia for tens of thousands of years before it was colonised by mostly white English settlers in the 18th Century.
The line to be removed in the anthem, which is called Advance Australia Fair, is "For we are young and free". Instead people will sing "For we are one and free."
Earlier this year, the leader of New South Wales state, Premier Gladys Berejiklian, suggested the change, saying the current wording ignored Australia's "proud First Nations culture".