Tariq al-Farrah, spokesperson at the Indonesian embassy in Amman, said on Tuesday the trio had arrived in the Jordanian capital and were safe and in good health.
Earlier, Mahmud Abu Fadala, the brother of the driver, had said the three people had been stuck on the Iraqi side of the border, as it was sealed for the Shia Muslim mourning period of Ashura.
Originally they were informed by the authorities that the Iraq border would remain closed until at least midnight.
But in the last few hours, border guards were given new instructions to allow the trio through as an exception.
Iraq has had its borders closed since 17 February, citing security concerns for the period of Ashura.
Indonesian reporters Meutya Hafid and cameraman Budiyanto of Metro TV news channel were seized along with their Jordanian driver on 15 February as they drove from Jordan to Baghdad.
Their captors freed them on Monday in Ramadi, west of the Iraqi capital Baghdad.