Saudi Arabia and on Wednesday hailed decision to revoke its recognition of West Jerusalem as capital.
Australian Foreign Minister Penny Wong on Tuesday said Jerusalem's status should be decided through peace talks between Israelis and Palestinians, and not through unilateral decisions.
Most of the international community do not recognise Jerusalem as Israel's capital, maintaining embassies in Tel Aviv.
Israel conquered the Palestinian eastern half of the city during the 1967 Arab-Israeli war and illegally annexed it.
The Saudi foreign ministry shared a statement on Twitter saying Riyadh "welcomed" the Australian reversal.
The kingdom urged "the international community to combine efforts to find a just settlement of the Palestinian issue to achieve the aspirations of the brotherly Palestinian people to establish their independent state with East Jerusalem as its capital, in accordance with international legitimacy resolutions and the Arab Peace Initiative".
Jordan's foreign ministry tweeted a separate statement saying it "welcomed" the Australian move.
The statement said this included Canberra's decision "not to move its embassy from Tel Aviv to Jerusalem".
Wong said: "Australia's embassy has always been, and remains, in Tel Aviv."
A now-removed line on the Australian foreign ministry website had previously said: "Australia looks forward to moving its embassy to West Jerusalem when practical, in support of, and after the final status determination of, a two-state solution."
Sinan Al-Majali, a spokesperson for the Jordanian foreign ministry, "praised Australia's positive stance" as being "in line with international law".
"[He said] this stance is consistent with efforts aimed at reaching a just and comprehensive peace," the foreign ministry added in a statement.
Jordan expressed support for a two-state solution establishing a Palestinian state with East Jerusalem as its capital and its borders as they were before the 1967 Arab-Israeli War when Israel captured the whole city.
Palestinian Authority Civil Affairs Minister on Tuesday also backed Australia's move.
"We welcome Australia's decision with regards to Jerusalem & its call for a two-state solution in accordance with international legitimacy," he tweeted.
Agencies contributed to this report.