Rouhani's first official visit to Russia comes as the two Syrian regime supporters push for ways to end the six-year conflict, having done much to marginalise US influence in peace talks.
Iranian Foreign Ministry spokesman Bahram Ghasemi said ahead of the trip that the leaders would discuss "regional issues especially the Syrian crisis, solutions to end it quickly," as well as ways to counter "terrorism and extremism."
Rouhani -- accompanied by Foreign Minister Mohammad Javad Zarif and Oil Minister Bijan Zanganeh and other high-ranking officials -- is expected to sign more than 10 economic cooperation agreements with Russia, according to Iranian state media.
The Kremlin said in a statement this month that Rouhani's trip would focus in part on "the prospects of expanding trade, economic and investment ties."
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In addition to cooperation on Syria, energy and defence ties between Iran and Russia have grown despite meagre trade relations.
Russia is to build nine of Iran's 20 nuclear reactors in the coming years and has also emerged as a long-term arms partner for Iran, supplying Tehran with the S-300 air defence system.
Rouhani is looking to boost Iran's economy ahead of elections in May in which he is expected to stand for a second term.
Iran and Russia have become increasingly allied in Syria, providing support that has propped up President Bashar al-Assad.
They helped Assad's forces gain ground in recent months, including in the Syrian army's major offensive last year to retake rebel-held eastern Aleppo.
More than 310,000 people have been killed since conflict broke out in Syria in March 2011 with protests against Assad's rule.