Mr Shorten said he had phoned Mr Turnbull to concede defeat as it had become clear the Coalition would be able to form government.
Deputy Prime Minister Barnaby Joyce says the coalition also has three years to make sure people know that there is no intention whatsoever to privatise Medicare.
Former Australian leader Paul Keating once said Mr Turnbull was brilliant and fearless, but had no judgment.
The election was not, however, entirely resolved.
Although he is expected to form a majority government, Turnbull's gamble in calling the election backfired badly, with a swing to the centre-left Labor opposition and a rise in the popularity of minor parties and independents.
According to ABC News Australia's count, the Coalition has won 74 seats and Labor 66, with five still undecided.
Shorten told reporters that he called Turnbull on Sunday to congratulate him on the victory.
The opposition Labor Party has secured 69 seats so far, falling short of the seats needed to govern in Canberra even with the support of independent candidates.
He said "where there is common ground", Labor would work together with the coalition.
Australians usually know who their next leader will be on the night of their vote, but the July 2 poll was too close to call, triggering a complicated system of centralized vote counting that still hasn't technically finished.
Independent MP Andrew Wilkie said on Saturday he would not do any deals with the major parties after Queensland independent Bob Katter and Victorian independent Cathy McGowan pledged to give supply and confidence to the coalition earlier this week.
"That's a moment I'll never forget", an emotional Mr Turnbull said.
"None of us should have a tin ear to the public's view about a number of issues, including superannuation", Immigration Minister Peter Dutton told the Daily Telegraph newspaper, referring to proposals on tax breaks for pensions.
A full eight days after Australia quickly ticked boxes before their democracy sausages, this never-ending election is finally over.
Australia voted in the Liberal Party's Tony Abbott in 2013, who was beaten in a leadership challenge by Turnbull just two years later as his popularity plunged.
"I understand we need to make this parliament function and we'll be up for that".