Opposition Leader Bill Shorten phoned Mr Turnbull on Sunday to concede defeat and congratulate him.
Mr Shorten has reassured voters that the ALP will still pursue its core values and promises, but also pledged to work with the Coalition where possible.
Meanwhile .. Mr Turnbull says he expects his ministry to be sworn in next week .. but hasn't flagged a major shake-up.
"I've obviously given consideration to the ministry - both before and after the election and as you know I've said the ministry I lead - I led to the election will be the ministry I lead after the election. Regretably several ministers have not been returned and so there will some some changes. But you shouldn't anticipate large scale changes. The Ministry was assembled relatively recently following the retirement of Warren Truss."
Prime Minister Malcolm Turnbull claimed victory on Sunday after Bill Shorten rang him to concede Labor had lost.
The coalition is on track to win at least 76 seats as counting continues in five seats that are separated by less than 500 votes.
Labor could win 68 seats and the Liberal-held Queensland electorate Herbert is going down to the wire.
Mr Turnbull has arrived in Canberra to determine his new ministry.
He'll have to replace at least three junior ministers who have lost their seats.
There is pressure on him to promote rising stars from the coalition's conservative wing, as well as give the Nationals another cabinet spot on the back of the party's strengthened vote.
Senior Liberal M-P Mathias Cormann says the line-up of the new ministry is entirely in the hands of the Prime Minister.
Though he says he believes Tony Abbott has taken himself out of the race.
"Tony Abbott himself has said that he's not seeking to get back into the Cabnet. He's played a very positive and very constructive role during this campaign. He is setting out what he seeks to do in the next parliament as the member for Warringah and no doubt as a highly regarded and highly respected elder statesman of the party and obviously he's been very clear in terms of his intentions but the make-up of the cabinet is entirely a matter for the prime minister."
