Under the terms of the deal, Zimbabwe will be able to sell some stockpiles.
It may be able to resume full exports after a review of conditions at the Marange diamond fields in September.
The Kimberley Process suspended the diamond exports in November in response to allegations of atrocities committed by security forces at Marange.
There have been weeks of deadlock over the negotiations and the deal in Russia came only after a Zimbabwean human rights activist was released on bail earlier this week.
Farai Maguwu is accused of providing false information about the diamond trade and was arrested after meeting a representative of the Kimberley Process on 3 June.
His continued detention scuppered attempts to reach a deal on Zimbabwe’s diamond exports at a Kimberly Process meeting in Israel last month.
Campaigners said a crisis had been averted by a last-minute deal.
‘Battered integrity’
“The ball is now in Zimbabwe’s court to make good on its promises and act to end one of the most egregious cases of diamond-related violence for many years,” Annie Dunnebacke of Global Witness said in a statement.
“We fervently hope that the governments in the Kimberley Process will, for their part, hold Zimbabwe to its commitments in order to begin to restore the battered integrity of the scheme.”
Zimbabwe Mines Minister Obert Mpofu said the country was “ready and willing” to work with the Kimberly Process.
“We know the value of co-operating with the organisation,” the Wall Street Journal quotes him as saying.
The army took over the Marange mines in 2008 and has since been accused of committing widespread abuses there – killing some 200 miners and forcing others to work in the mines.
West accused
Campaigners say the diamond money is being used to fund President Robert Mugabe’s Zanu-PF party.
Zimbabwe’s army has denied the allegations.
In February, President Mugabe threatened to leave the Kimberley Process after Zimbabwe was given until June to prove that its mines were properly run.
The Kimberley Process was set up in 2002 after the diamond trade was accused of fuelling several conflicts in Africa.
The diamonds from the Marange field could see the country become one of the world’s top six exporters and generate $1.7bn (£1.1bn) a year.
Zimbabwe has accused the West of trying to hold back its economic development.