Opposition Labor Leader Bill Shorten has conceded defeat and congratulated his opponent.
Votes are still being counted, but the Liberal-National coalition is expected to win enough seats to govern.
However, a strong swing against it has left doubts about its agenda and Turnbull’s leadership.
The coalition still remains short of the 76 seats it needs to claim a majority in the lower house, the House of Representatives.
But it should secure at least 74, and also has the support of three independent and minor party politicians guaranteeing budget supply and confidence.
Labor is currently on 66 seats, with five still in doubt.
At a news conference, Turnbull said: “We have had a successful election. We have secured the largest number of seats in parliament.”
“We have resolved this election and have done so peacefully. It’s something we should celebrate and not take for granted.”
He admitted that the election was “a tough business”, but welcomed Shorten’s calls for “common ground” in parliament.
The prime minister said he welcomed that offer and would work with Labor to try and fund essential services while balancing the budget.
“These challenges are not easy, there’s no simple solution, but that’s why they need our best minds, our best brains, above all our best goodwill in our new parliament to deliver that,” he said.
Shorten finally admitted defeat at the weekend. He had previously acknowledged the Coalition was likely to “scrape” over the line but had not officially conceded defeat.
He said he now respected Turnbull has a mandate to pursue his policies but that Labor also has its own mandate from voters to defend its values.
“I understand we need to make this parliament function and we’ll be up for that. I hope for the nation’s sake that the Coalition does a good job.”
But he added the ALP would be sticking to its guns on key issues such as Medicare.
“I expect them to do nothing less than to keep their promises they made to the Australian people,” he said.
Shaun Davies, Australia Editor for BBC News said Turnbull has his majority, but he is beset on all sides.
“The prime minister has his party’s support for now, but his enemies are watching closely.
“Former Australian leader Paul Keating once said Turnbull was brilliant and fearless, but had no judgment. The prime minister can’t afford to put a foot wrong now.
“The tight result is likely to put pressure on the government’s agenda, particularly in the Senate, where many independent and minor party candidates are set to take office.
“Conflicting agendas and strong personalities could make it difficult for Turnbull to pass legislation through the Senate,” Davies commented.
Turnbull has come under pressure both internally and externally since the worse-than-expected election result became clear.
Senator Cory Bernardi, one of the coalition’s most vocal right-wingers, called the election “a disaster” and has since made moves to establish his own conservative movement, although he denies plans to defect from the Liberal party.
On Thursday ratings agency Standard & Poor’s lowered Australia’s credit rating outlook from stable to negative, warning the country could lose its AAA rating unless it undertook budget repair.
Treasurer Scott Morrison described the downgrade as “sobering” and said the government’s budget savings needed to be implemented.
But shadow treasurer Chris Bowen said the opposition would campaign against any spending cuts that would hurt Australians on low incomes.
Doubts have been raised over the passage of government’s Australian Building and Construction Commission bill, which aims to re-establish a watchdog that monitors union activity in Australia’s building industry.
Independent MP Bob Katter has already indicated that he will withdraw his support from the government if it engages in what he sees as “union bashing”.
The Australian-Chinese community has launched a social media campaign to try to combat what it describes as intolerant and racist ideas being spread by senator-elect Pauline Hanson.
Community leaders said when Hanson was last in parliament 20 years ago, they documented a significant increase in the number of people of Asian heritage being verbally and physically abused by strangers in public. - PNC sources