The March 5-8 visit - the first ever by a pope - will include stops in Baghdad, Najaf, Nasiriya, Erbil, Mosul and Qaraqosh, according to the official itinerary published by the Vatican.
On March 6, the pontiff is scheduled to make a "courtesy visit" to the 90-year-old Sistani in Najaf.
The pope had previously suggested his visit to Iraq might be cancelled because of the coronavirus pandemic, but on Monday, made clear his desire to go.
"I myself wish to resume my Apostolic Visits, beginning with that to Iraq," he told ambassadors to the Holy See.
"These visits are an important sign of the solicitude of the Successor of Peter (the pope) for God's People spread throughout the world and the dialogue of the Holy See with states," he said.
"They also frequently provide an opportunity to promote, in a spirit of sharing and dialogue, good relations between the different religions."
Inter-religious dialogue, he added, "can become an opportunity for religious leaders and the followers of different confessions, and can support the responsible efforts of political leaders to promote the common good".
Last month, the patriarch of Iraq's Chaldean Catholic Church Louis Sako said the pope would have a private visit with Sistani, who is never seen in public and rarely accepts visitors.
Sako said then he hoped the two religious leaders would sign the document on "human fraternity for world peace", an inter-religious text condemning extremism that Francis signed in 2019 with the leading Sunni cleric Sheikh Ahmed al-Tayeb, the grand imam of Al-Azhar.
Iraq once counted more than 1.5 million Christians but today only an estimated 400,000 Christians remain after being ravaged by violence, most recently sectarian warfare that followed the 2003 US-led invasion and attacks by Islamic State.
Francis plans to celebrate Masses at Baghdad in a cathedral that was the site of a 2010 bloody attack and in a stadium in Erbil, the capital of Iraq's Kurdish region, where many Christians have fled after being displaced by Islamic State.
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