Ms Bishop said in a statement this afternoon that she will remain on the back bench "as a strong voice for Western Australia".
Morrison replaced Turnbull in a party-room vote after a week of political chaos in Canberra that marked the emergence of Australia's sixth prime minister in less than 10 years.
Mr Turnbull praised Ms Bishop, saying she "has been and remains an inspiring role model for women here and around the world".
Curtin MP Julie Bishop's decision to quit cabinet and the coveted foreign affairs portfolio is perhaps the biggest unintended outcome of Malcolm Turnbull's demise.
Mr Shorten wrote to Prime Minister Scott Morrison on Monday to ask him to extend the tenure of the current Governor-General, Peter Cosgrove, beyond the next election so that the choice of his replacement would be delayed.
It follows Julie Bishop's decision to stand down from the role following the turfing of Malcolm Turnbull as Prime Minister late last week.
Labor's Penny Wong also paid tribute to Ms Bishop for her "trailblazing role as the first Australian woman to be Minister for Foreign Affairs".
One of the casualties was Labor's Julia Gillard, Australia's first female leader, who constantly battled misogyny and made worldwide headlines for her fiery rebuttal of then Liberal opposition leader Tony Abbott in parliament in 2012.
"Due to the high turnover of prime ministers, we can not see ourselves making a figure of a sitting Australian prime minister again", Mark Connolly, the general manager of the Sydney branch, said.
"The last week was a very hard week for the party and my colleagues but we do need to move on".
On Sunday, the super-fit 62-year-old ran in Perth's City to Surf race before announcing she was calling time on her successful tenure as foreign minister.
Nationals MP Keith Pitt also quit on Sunday as the Assistant Minister to the Deputy Prime Minister, protesting the government's efforts to address climate change and its commitment to the Paris agreement.
"It's nearly a deafness that we still see in Australian society", she said.
His party will already have to contest a by-election for Turnbull's harbourside electorate in Sydney, traditionally a safe Liberal seat.
Mr Abbott was last week accused of being a "wrecker" by fellow Liberal MPs for laying the groundwork for the sudden move by the party's conservative wing against Mr Turnbull.
Insiders host Barrie Cassidy, who revealed the messages, said Ms Bishop was "entitled to be embarrassed and angry".
Lewandowski: I warned Trump about Cohen
President Donald Trump has some advice for Trump if he is considering whether to pardon his former campaign chairman: don't do it. Separately, the NY state attorney general has filed a civil lawsuit against the Trump foundation, Trump's purported charity.
Health- Get glowing skin with potatoes
Exfoliation : At times we feel like our skin is just too shiny, no matter how much makeup we apply. If you follow the below steps religiously, your skin texture will improve within a few weeks.
Gambling Games with Friends
Payouts at online casinos are higher than at land-based casinos even though the chip sizes are lower at internet casinos. There are image detection technology and motion technology involved in making the complete package work and it works.
Google Fire’s Guy For Memo
A memo that has brought more attention to the very critical issue that is rocking Silicon Valley and indeed the rest of the world. Should the guy dare complain, he is branded with the vilest descriptions?Rather stay at home and enjoy casinos online .