The development enables resumption of talks that stalled after Moscow demanded assurances that sanctions over Ukraine won’t impact its ties with Tehran.
Moscow has received guarantees from Washington on its ability to trade with Tehran as part of ongoing talks to salvage the Iran nuclear deal.
"We received written guarantees. They are included in the text of the agreement itself on the resumption of the Joint Comprehensive Plan of Action on the Iranian nuclear programme," Russia's Foreign Minister Sergey Lavrov said at a press conference in Moscow with Iranian counterpart Hossein Amir-Abdollahian on Tuesday.
More than 10 months of talks in Vienna have brought major powers close to renewing the landmark 2015 Joint Comprehensive Plan of Action (JCPOA) on regulating Iran's nuclear programme.
The negotiations halted after Moscow earlier this month demanded guarantees that Western sanctions imposed following its military operation in Ukraine would not damage its trade with Iran.
Lavrov said that the guarantees it had received from Washington would protect Russian involvement in Iran's sole Bushehr nuclear energy plant.
The minister said Moscow and Tehran share the position that Western sanctions are imposed with the aim of overriding international law and accused Washington and its partners of directing the penalties "primarily against ordinary citizens".
The 2015 deal gave Iran sanctions relief in exchange for curbs on its nuclear programme.
The agreement aimed to ensure Iran would not be able to develop a nuclear weapon, which it has always denied seeking.
"Russia will not be an obstacle to reaching an agreement," Iran's Amir-Abdollahian said at the press conference with Lavrov.
"There will be no relation between Ukraine's developments... and Vienna negotiations," he said, referring to the ongoing conflict and talks on renewing the 2015 agreement.
He praised Russia's "very positive and constructive role" in the talks and said Moscow would "stay beside the Islamic Republic of Iran until the end of the negotiations and reaching a good, strong and lasting agreement".