The trip, described as "historic and noble" by Iran's Foreign Minister Mohammad Javad Zarif, will strengthen ties between the neighbouring states.
Rouhani's visit comes following a string of high-level visits between Iranian and Iraqi officials in recent months.
Iran and Iraq fought a devastating 1980-88 war but the 2003 US -led invasion of Iraq that ousted Saddam Hussein prompted a long Sunni Islamist insurgency during which Iran's regional sway rose at the expense of the United States.
Zarif said that during Rouhani's three-day visit to Iraq, the President would meet with chief Shiite cleric Ali Sistani.
Salih was speaking in Baghdad ahead of a visit by Iran's President Rouhani.
Shiite-majority Iraq is walking a fine line to maintain good relations with its key partners Iran and the United States which themselves are arch-foes.
The Iranian president said, "We are awaiting your strong action against these terrorists".
Those ties "cannot be compared to Iraq's relations with an occupying country like America, which is being hated in the region", the semi-official Mehr news agency quoted him as saying before he left. "The bombs that the Americans dropped on Iraqis, Syrian people and other countries can not be forgotten", he added.
Tehran sees the United States military presence at its doorstep in Iraq as a threat - one that could also undermine Iran's influence over Baghdad.
"We are very much interested in expanding our ties with Iraq, particular our transport co-operation", Mr Rouhani said later. But the government supports powerful Shi'ite paramilitary groups operating in the country, with estimates of the number of fighters ranging up to 150,000.
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"I have briefed Prime Minister Imran Khan about meetings during the visit of Iran", Rasheed told media here today.
He will visit a Shia shrine in the Iraqi capital and then meet President Barham Salih and Prime Minister Abdel Abdul Mehdi, as well as visit other politicians and Shia leaders.
In 2018, Iran's exports to Iraq came to about $9 billion, while an estimated 5 million religious tourists create some $5 billion a year in economic benefits as Iraqi and Iranian citizens visit Shi'ite holy sites in the two countries.
In 2013, the Grand Ayatollah refused to receive Mr Rouhani's controversial predecessor Mr Ahmadinejad.
Rouhani was received by an honor guard on landing in Baghdad, where he was welcomed by Iraqi Foreign Minister Mohammed Ali Al-Hakim.
The Iranian president is facing pressure from hardliners at home after Mr Trump pulled out of the nuclear deal with Tehran.
Iranian President Hassan Rouhani has joined cause with India and stepped up pressure on Pakistan by asserting that Pak-based sources & sponsors of cross-border terror funding are "well-known" and warned that inaction against terror groups will undermine Iran-Pak ties.
But Iraq has taken a firm stance against the embargo and said it would "stand by Iran".
"Iraq is another channel for Iran to bypass America's unjust sanctions imposed on Iran".
Iraq relies on Iranian gas imports to feed its power grid and has asked for extensions to a U.S. waiver to continue importing Iranian gas since U.S. President Donald Trump restored sanctions on Iran's vital energy sector in November.