She says, "Today I advised the prime minister that I will be resigning from my Cabinet position as minister for foreign affairs".
Scott Morrison has offered Tony Abbott a role as special envoy for indigenous affairs, but the former prime minister is yet to accept the appointment.
Ms Bishop contested Friday's leadership vote but was eliminated in the first round, with Mr Morrison then emerging as a surprise compromise victor over Peter Dutton, Mr Turnbull's conservative challenger who brought the leadership crisis to a head earlier in the week.
The former treasurer was sworn in as Australia's 30th Prime Minister yesterday evening after a tumultuous few days.
The City of Sydney councillor said she had a strong record of championing Liberal Party values at a local government level.
The possibility that Ms Bishop could leave Parliament before the next election will be a major concern for Mr Morrison, Mr Turnbull's former treasurer, because it opens the possibility of another by-election being held for her seat.
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.
Mr Dutton, whose first challenge on Tuesday sparked the crisis that ultimately toppled Mr Turnbull, returns as home affairs minister in an apparent attempt by Mr Morrison to rebuild unity in his badly bruised party.
Since her resignation, supporters of the former deputy have paid tribute to her career.
Scott Morrison won and Julie Bishop was left embarrassed and betrayed by the party she had served so faithfully for decades.
'For five years she has dedicated her life to our nation with a tireless work ethic and exhausting travel schedule.
She said that while Labor had at times been critical of the Government's foreign policy directions "Ms Bishop's commitment to standing up for Australia both here and overseas has never been in question".
"Australia is New Zealand's most important partner", said Ms Ardern.
"I don't find the need to self-describe in that way [as a feminist]", she famously said in an address to the National Press Club in 2014.
'Proof the boys-club still have a stranglehold on politics, ' Ms Hanson Young said.
It is understood her only request of Mr Morrison was that NSW senator Marise Payne should succeed her as Foreign Minister. It's a hard job.
Federal member for Chisholm, Julia Banks said: 'In Julie Bishop our nation has been gifted with a fine leader and a standout role model for girls and women'.