"The prime minister of Jordan has arrived accompanied by Foreign Minister Faruq Kassrawi," an official source in the president's office said.
Badran was expected to hold a joint news conference later on Saturday with Iraqi Vice President Adel Abdul Mehdi, the official said.
The previously unannounced visit is the first by a high-ranking official from Iraq's western neighbour, which hosts Saddam's family.
Jordan is a major port of entry for goods and people into Iraq, which had been Amman's primary source of oil.
Jordan withdrew its ambassador to Iraq shortly after three diplomats - two Algerians and an Egyptian - were captured in July and killed. Al-Qaida in Iraq, led by Jordanian-born Abu Musab al-Zarqawi, claimed responsibility.
Fighters have also fired on diplomats from Pakistan and Bahrain in what police described as apparent kidnap attempts. The Pakistani escaped unharmed and the Bahraini was slightly wounded.
Kidnappers attempted to seize a
Bahraini diplomat in Iraq
After the attacks, the Philippine embassy in Baghdad relocated its staff to Jordan.
Last month, Jordan nominated an ambassador to Baghdad, and Iraq has accepted the nominee. Jordan delayed sending its new envoy until the Iraqi capital was more secure.