Bishop received 11 votes in Friday's leadership ballot - coming in behind both Prime Minister Scott Morrison and former Home Affairs Minister Peter Dutton - in a surprise result, given that she is popular amongst voters and well regarded in the worldwide diplomatic circuit.
She had sought the prime minister's job after Malcolm Turnbull stood aside, but was eliminated in the first round.
Morrison flew to rural western Queensland state, where crops are failing and ranchers are struggling to feed sheep and cattle after six years of drought. In 2015 the Abbott camp felt betrayed, believing that Scott Morrison had not backed him wholeheartedly, despite being a Christian conservative.
"The powerbrokers of the Liberal Party have ignored the people's wishes on Mr Turnbull and they've ignored the people's wishes on Julie Bishop".
The latest Newspoll, published by The Australian newspaper, also showed opposition Labor leader Bill Shorten, who had long trailed Mr Turnbull, is now preferred prime minister.
Mr Buchholz, the Member for Wright, has been appointed Assistant Minister for Roads and Transport in the Morrison Government.
The Energy and Environment has also been split, with Melissa Price becoming the Environment minister, while Angus Taylor was given the Energy role. His contender Peter Dutton will keep his Home Affairs role, but the Immigration will go to David Coleman.
The new foreign minister's big challenge will be navigating a tricky relationship with China, Australia's top trading partner.
If the reports are correct, Turnbull's resignation will trigger a by-election in his seat of Wentworth, eastern Sydney, with several potential candidates already emerging.
"While Labor has at times been critical of the foreign policy directions under prime ministers Abbott and Turnbull, Ms Bishop's commitment to standing up for Australia both here and overseas has never been in question".
Deputy Prime Minister Michael McCormack said the polls reflected a week of division and disorder.
The announcement comes as Morrison looks to quickly move the government away from a hellish week for the government which ultimately saw Malcolm Turnbull from power.
"This new Liberal-National team is a next-generation team", new Prime Minister Scott Morrison said.
"For all the fierce words of disagreement, I do not doubt for one second that Mr Turnbull was a loyal servant of Australia", he said.
Prime Minister Scott Morrison and Deputy Leader Josh Frydenberg.