Morrison and his Cabinet team, which includes a record seven women, visited the Government House where the Governor General Peter Cosgrove swore them into office.
Ken Wyatt, an Aboriginal Member of Parliament from Western Australia, received a standing ovation as he became the country's first Aboriginal Cabinet minister. He will be in charge of indigenous affairs, ABC News reported.
Wyatt wore a traditional kangaroo skin called a "booka" to the swearing-in ceremony.
Morrison's Liberal-National Party Coalition (LNP) defied polls to win a third term in government in the general election on May 18, defeating the opposition Australian Labour Party (ALP).
He elevated Sussan Ley, Linda Reynolds and Anne Ruston to his Cabinet the government's council of senior ministers as the Ministers for the Environment, Defence and Families and Social Services, respectively.
They joined Foreign Affairs Minister Marise Payne, Agriculture Minister Bridget McKenzie, Employment Minister Michaelia Cash and Industry Minister Karen Andrews as women in Cabinet.
Australia's 46th Parliament is expected to convene for the first time in the first week of July, with the Electoral Commission still counting votes.
In the first post-election meeting with coalition MPs on Tuesday, Morrison insisted his "hungry, committed and united" team would focus on the aspirations of ordinary Austral during their third term in power.
"They are the reason we have the opportunity and the great privilege to serve them each and every day," the Prime Minister told his colleagues.
"We must burn for the Australian people every single day that we have this privilege of serving them, in this party room and as a government."
Morrison warned his ministers that there was a wealth of talent within the government's ranks to keep the pressure on them to perform.
( With inputs from IANS )