At a joint news conference, Mr Rouhani said: "We want to forge very close relations with Iraq".
"Rouhani is coming to discuss. trade between the countries (and) the issue of easing trade exchanges in Iraqi local currency and finding other ways, like Germany and Britain, to adopt an alternative European currency to circumvent U.S. sanctions", Iraqi political analyst Hisham al-Hashemi told AFP.
The southeastern region of Iran is facing a rise in attacks by militants from the Sunni Muslim minority.
Rouhani´s visit to Iraq will be the first since he became president in 2013.
The president is expected to meet with Iraqi President Barham Salih and Prime Minister Abdel Abdul Mehdi, as well as visit other politicians and Shiite leaders.
Have Iran-Iraq ties always been good?After the 2003 US-led invasion of Iraq toppled Saddam, Iran began a campaign of backing militants who targeted American forces in Iraq.
Iraq discontinued crude oil swaps with Iran in October and did not receive an exemption when a new wave of sanctions came into effect the following month.
Iranian President Hassan Rouhani is seen during a public speech in the northern province of Gilan, Iran March 6, 2019.
Iran wields influence in Iraq through its economic footprint and extensive ties to Iraqi political groups, Shiite militias and the country's elite.
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According to Iranian readout, Prime Minister Khan assured that his government will not allow terrorist to use his country's soil against neighbours especially Iran and "will do their best to eliminate the terrorists". It will also send a strong message to US President Donald Trump and regional allies that Tehran still dominates Baghdad, observers say.
"Iran wants to build upon the opportunity of sanctions waivers, and by consolidating the existing level of economic ties with Iraq and enhancing the level of interdependency, makes it even harder for the United States to convince Iraq to change its course regarding the Islamic Republic", he added.
Rouhani, who had visited Iraq privately before becoming president, had planned an official visit in 2016 but it was cancelled over unspecified "executive" problems.
Iran also sees Iraq as a possible route to bypass United States sanctions that Trump re-imposed a year ago after pulling the USA out of the 2015 nuclear deal.
Prime Minister Imran khan expressed his heartfelt condolences on the recent terrorist attack in which 27 Iranian guards were killed.
Iranian Foreign Minister Mohammad Javad Zarif, who arrived in the Iraqi capital earlier in the day, thanked Baghdad for having "refused the unjust and illegal sanctions imposed on the Iranian people", in reference to the US sanctions.
From Baghdad's perspective, she added, "Iraq seeks to balance its relations between the USA and Iran by not angering the former or provoking the latter".
Mr Rouhani's visit also indicates how relations between the two states have changed.