The summit aims to bring the United State’s two rivals closer together as they work on a variety of different issues.
Mr Putin and his Iranian hosts are expected to discuss the controversial and endangered 2015 Iran nuclear deal and regional crises such as the Syrian conflict, in which Russia and Tehran are the main backers of President Bashar al-Assad.
Washington, Turkey and most Arab states, however, support opposition groups seeking to overthrow him.
Iranian President Hassan Rouhani said: “We are very pleased that, apart from our bilateral relations, our two countries play an important role in securing peace and stability in the region.”
The most important issue for both states, however, will be the threat posed by Donald Trump and the USA – particularly with regards to the 2015 Iran nuclear deal.
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Mr Trump slated Tehran during his election campaign and has now threatened not to renew the deal, which he said was one of the worst ever made.
Moscow is an important ally for Iran in its confrontation with the Trump administration and has criticised the move strongly.
Mr Trump’s decision has opened a 60-day window for Congress to reimpose economic sanctions on Iran. These were lifted under the 2015 accord in return for Tehran curbing its nuclear programme.
One Tehran official said: “This is a very important visit. It shows the determination of Tehran and Moscow to deepen their strategic alliance which will shape the future of the Middle East.
“Both Russia and Iran are under American pressure. Tehran has no other choice but to rely on Moscow to ease the U.S. pressure.”
Another official said America’s aggressive Iran policy had united Iran’s faction-ridden leadership in alignment with Russia.
Russia has already pledged support for the Iran deal – even if the USA pulls out.
The Iranian offical said: “We are going to support this deal. We are going to support the deal concluded with the previous US administration, although as you know we had many differences with them on other issues.
“It is not Russia that defines or predetermines that Iran is in compliance with its commitments, that is for the IAEA. According to IAEA reports, as of now all other countries are in compliance.”
“We are very much respectful of the national interests of Iran.”
During his visit, Mr Putin will also discuss boosting bilateral economic ties, and will take part in a three-way summit between Russia, Iran and neighbouring Azerbaijan, state TV said.