Ms Bishop was a highly visible presence on the world stage, regularly stepping into the lead role at summits and other gatherings when prime ministers Malcolm Turnbull and Tony Abbott were unable to attend.
The Trump administration, after building strong bonds with Mr Turnbull and Ms Bishop, will now attempt to forge similar partnerships with former treasurer and new prime minister Scott Morrison and Ms Bishop's replacement, Defence Minister Marise Payne.
"We worked very closely with former prime minister Malcolm Turnbull and enjoyed a very positive relationship with him and Foreign Minister Julie Bishop," a State Department spokesperson told AAP on Sunday.
Julie Bishop has quit as Foreign Minister. Source: AAP
"This included an official visit by the prime minister to the White House in February and hosting Foreign Minister Bishop for the Australian-US Ministerial (AUSMIN) Consultations in Palo Alto in July.
"We are grateful for their service to the alliance and wish them all the very best going forward.
"We are confident that the close working relationship under Prime Minister Morrison will continue."
Bishop resigns
Prime Minister Scott Morrison had wanted Julie Bishop to stay on as foreign minister but accepted her decision to step aside.
Ms Bishop issued a statement on Sunday afternoon announcing her decision following last Friday's change of prime minister.
But she left open the question about how long she would stay in parliament.
"Today I advised the prime minister that I will be resigning from my cabinet position as Minister for Foreign Affairs," she said.
"I will remain on the backbench as a strong voice for Western Australia.
"I have been pre-selected by the Liberal Party for the seat of Curtin and I have made no decision regarding the next election."
Mr Morrison announced defence minister Marise Payne will take over foreign affairs on the recommendation of Ms Bishop.
"I would have very much welcomed her continuing role in the ministry, but totally understand and respect the decision that she has made," Mr Morrison said.
Ms Bishop, 62, was deputy Liberal leader for more than a decade but she only received 11 votes in last Friday's leadership ballot after Malcolm Turnbull called a spill.
Mr Turnbull on Sunday described her as Australia's finest foreign minister and thanked her for her loyalty and friendship.
"She has been and remains an inspiring role model for women here and around the world," he tweeted.
Ms Bishop's Labor counterpart Penny Wong paid tribute to her for her trailblazing role as the first Australian woman to be foreign affairs minister.
"For five years she has dedicated her life to our nation with a tireless work ethic and exhausting travel schedule," Senator Wong said.
"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 abroad has never been in question."
Former prime minister and foreign minister Kevin Rudd also tweeted Ms Bishop had been a highly effective Australian foreign minister.
" ... she has earned, absolutely, the respect of foreign ministers around the world," he said.
British High Commissioner to Australia Menna Rawlings she was sad to hear of Ms Bishop's resignation.
"She has been a gutsy, dynamic, representative of Australia. And a fantastic friend of GB (Great Britain)," she tweeted.
Cabinet minister Simon Birmingham earlier on Sunday said Ms Bishop was "the most significant woman in the history of the Liberal Party" and deserved to make a decision about her future without external pressure.
Ms Bishop, who is renowned for her fitness and energy, announced her resignation after finishing City to Surf fun in Perth with a personal best time.
Malcolm Turnbull has described Julie Bishop as Australia's finest foreign minister. Source: AAP
