Al-Jaafari is expected to meet all of Turkey's top leadership, including President Recep Tayyip Erdogan, during his three-day visit and started the trip by holding talks with Foreign Minister Mevlut Cavusoglu.
Relations between Ankara and Baghdad soured badly in the final years of al-Maliki's rule, with Erdogan accusing the former premier of bearing the blame for Iraq's security chaos.
The Iraqi government was also angered by the assistance given by Turkey to the autonomous Kurdistan region in seeking to export its own oil, which Baghdad said was illegal as it belonged to the state.
"The problems in Iraq were caused by the previous administration," Cavusoglu told reporters at a news conference with Jaafari.
"We want to improve our political and economic relations in this new process. In this regard, we welcome this new beginning in Iraq," he added.
In a sign of the improved ties, Turkish media said that the two sides had agreed to abolish all visa restrictions between them.
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Baghdad has looked with great suspicion on the flourishing trade relations between Turkey and the Kurdistan Regional Government (KRG).
It showed little enthusiasm over the despatch of Iraqi Kurdish peshmerga fighters, via Turkish soil, to join the fight against jihadists for the Syrian town of Kobane.
Jaafari made clear that the new government was sticking to the position that the KRG had no right to unilaterally export its oil through a pipeline via Turkey.
"According to the Iraqi constitution, oil sales is the business of the central government.
"We will sort out the problem with the Kurdish oil in line with the Iraqi constitution," he added.
Al-Jaafari, a key member of the new Iraqi government under Prime Minister Haidar al-Abadi, is a familiar figure to Ankara having himself been Iraqi premier from 2005-2006.
The Shiite Maliki stepped down in September after over eight years in power, bequeathing a dire security legacy with Sunni jihadists in control of swathes of the country.