The Russian defence ministry said it was now ready to supply the S-300 equipment "promptly", an official there said, quoted by Interfax.
The delivery would be a "step forward", for Russian and Iranian relations, the Iranian Deputy Defence Minister Reza Talainik told the Tasnim news agency.
"I think Russia has returned to the first step and is prepared to act upon its previous undertakings. We hope it will do so and show us its good will," he said.
Israel reacted with dismay to the news.
"This is a direct result of the legitimacy that Iran obtained from the emerging nuclear deal,'' said Intelligence Minister Yuval Steinitz.
He said it was "proof" Iran planned to use relief from sanctions for arms, rather than the welfare of the Iranian people.
The White House said US Secretary of State John Kerry had raised concerns with Mr Lavrov about the announcement, spokesman Josh Earnest said, without elaborating.