In Canberra, Prime Minister Malcolm Turnbull officiated at the national ceremony, observing that the 27 people from 13 countries were all volunteering to join the Australian family.
"Most of us arrived into the world screaming and squalling, conscripted into Australian citizenship," he said.
"I want to honour you, the volunteers at 400 ceremonies across the country, 16,000 new Australians just like you join our 24 million-strong family."
Mr Turnbull said Australia was the most successful multicultural society in the world, diverse and harmonious, with people from close to 200 countries.
"We can look at our past with great pride and with some regret, but we are not defined, let alone trapped by our history, as many other nations are," he said.
Among those taking Australian citizenship in Canberra was Diego Torres-Villegas, 37, a Mexican-born tenor with Opera Australia whose first official task as a new Aussie was to sing the national anthem live on television.
"Since 2011 my family are here. We have been every single time more and more attached to the country, meeting wonderful people and feeling more and more that this was our home," he told AAP.
Australian of the Year David Morrison, the former Army chief, was greeted at the Canberra event by flag-waving members of the group Muslims for Loyalty.
In an earlier interview, Mr Morrison said Muslims faced much discrimination.
"We need to understand the challenges they face. We need to see where the rest of Australia can work with them," he told the ABC.
In Melbourne, Opposition Leader Bill Shorten presided at the Brimbank Council citizenship ceremony in his electorate, welcoming 220 new citizens from 38 countries.
"Whether you are new to our shores or today is the final formal step in a long love affair with life in Australia, thank you for joining your story to ours," he said.
In Brisbane, Lord Mayor Graham Quirk officiated at the state's largest citizenship ceremony, welcoming 582 newcomers to the Australian family, urging those from war-torn or oppressive regimes to leave any sense of hatred behind.
"We are a country ... built on two very important things - respect for one another and harmony within our community," he said.
More than a thousand demonstrators marched in Sydney mourning the "day of killing" that accompanied the landing of the First Fleet 228 years ago.
Chanting "always was, always will be Aboriginal land", the protesters marched from The Block in Redfern to the centre of the city - with similar scenes replicated in "invasion day" marches around the nation.
