They did not specify which systems have arrived in Iraq or when, but Iraqi sources say it's understood they include 10 fully armed Mil Mi-28NE Night Hunter attack helicopters, platforms that could be a major boost to the counterterrorism efforts by the government of Prime Minister Nouri al-Maliki.
Russia's RIA Novosti news agency quoted Maliki's close aide Ali Musawi as saying "implementation of one of the contract's stages has begun" and systems involved were "mainly for anti-terrorist operations."
The 2012 contract marked Russia's return to a major Middle Eastern market it had dominated during the Soviet era. During Saddam Hussein's rule, that ended in April 2003, Moscow was Iraq's main arms supplier.
Under the 2012 contract, signed by Maliki during a visit to Moscow, Iraq is scheduled to get 30 of the all-weather Night Hunter helicopter gunships and 50 Pantsyr S-1 gun-missile short-range air-defense systems.
The helicopter contract covers pilot and technical personnel training and the delivery of "essential weapons systems."
At the time of the signing, the Moscow media reported further discussions for Iraq's eventual acquisition of Mikoyan MiG-29 interceptor jets, heavy armored vehicles and other weapons systems were under way.
But Iraq has already ordered 36 Lockheed Martin F-16Q Block 52 fighter jets, and has said it eventually wants to acquire as many as 96.
It was not clear why Maliki would want to split his planned force of combat jets between two such divergent suppliers, except possibly to hedge his bets in terms of big-power affiliations.
But operating a mix of U.S. and Russian weapons, rather than a standardized system, is incredibly complicated. Training, maintenance and logistics for two types of combat jets as different as MiG-29s and F-16s alone would be extremely expensive and cause supply nightmares.
The Mi-28NE is the export version of Russia's upgraded version of the Mi-28 attack helicopter, which is primarily a tank-killer. The model Iraq is buying is more flexible and can engage a wider range of targets, such as insurgents on the ground.
The Pantsyr S-1 combines surface-to-air missiles and twin-barreled anti-aircraft guns capable of engaging short-range and medium-range aerial targets.
The system is designed to operate in tandem with long-range SAMs like the S-400, Russia's most advanced and most powerful air-defense system, to protect strategic targets against airstrikes.
The Russians were especially pleased about the Mi-28 deal since it was the first foreign order for a system they'd been struggling to market without success.
Arms exports are a major revenue earner for Moscow and a key element in its drive to restore its Cold War influence in the Arab world.
President Vladimir Putin's support for the embattled Damascus regime in Syria, a major Cold War recipient of Soviet weaponry, is an important component of that strategy.
The 2012 deal was held up for several months after Musawi declared only one month after the contact was signed that the deal was being suspended because of suspicions of "corruption."
There were reports the deal had been scrapped, or was subject to renegotiation, while there was turmoil in Iraq's fractious Parliament amid heated debate over the 2013 budget.
After months of closed-door dealings between Moscow and Baghdad, the contract was resurrected and Maliki gave the Defense Ministry the go-ahead in March to proceed.
Baghdad made the first down payment, which allowed Russian production of the helicopters to begin. A new version of the contract was signed in Moscow March 25.
The Russians huffed at one point that the deal was being sabotaged by the Americans who wanted to keep Iraq's multi-billion-dollar arms procurement program for themselves.
Details of those corruption allegations remain unclear. But defense industry sources in Moscow said the Russians overcame Iraqi concerns by offering Baghdad four extra Mi-28s.
Iraqi lawmaker Ali al-Shala of Maliki's Rule of Law coalition said in April the new deal covers more advanced technology and systems that "will strengthen Iraq's air capabilities."