Scott Morrison now officially leads a minority government after independent Kerryn Phelps was formally declared the winner of last month's Wentworth by-election.

Prof Phelps, the former Australian Medical Association chief, defeated the Liberals' star candidate Dave Sharma by just over 1800 votes in one of the biggest ever by-election swings against a government.

It was forced by the resignation of former prime minister Malcolm Turnbull who held the seat in Sydney's ritzy eastern suburbs by just on 18 percent.

Dr Kerryn Phelps has been declared the official winner in the Wentworth by-election. (AAP)

Prof Phelps has listed climate change, asylum seekers on Nauru, and health, as key priorities she wants to discuss with the Prime Minister.

However she has said she doesn't want to be a "wrecker" and bring down the minority government.

She will join a powerful crossbench negotiating bloc with the likes of Rebekha Sharkie and Cathy McGowan that Mr Morrison will need to see legislation pass the House of Reps, and in fact, to cling to power.

Prime Minister Scott Morrison now leads a minority government. (AAP)

Prof Phelps is anxious for government briefings, particularly the fate of sick children and their families still on Nauru.

"Evidence is the most important thing," she said.

"I will make a decision based on those briefings."

She also wants to ensure private religious schools not be allowed to discriminate against teachers, as well as students, based on their sexuality, in any religious freedoms legislation.

Despite Prof Phelps win, Scott Morrison said the government will "continue to function".

"I don't think a lot has changed in terms of how many votes we have to get to pass legislation," he said.

"We still need 75. That's been the case the entire time I've been Prime Minister.