Health ministry spokesman Seif al-Badr told reporters that the first delivery in the early hours meant inoculations could begin.
“The doses will be delivered to Baghdad’s three main hospitals, and maybe to some provinces,” said Badr, who confirmed the jabs were donations.
“We will start vaccinations today, Tuesday,” he said.
The health ministry simultaneously announced it had agreed with the Chinese ambassador in Baghdad to purchase another two million doses, with no details on payment or timing.
Sinopharm affiliate Wuhan Institute Of Biological Products says its vaccine has an efficacy rate of 72.51 percent, behind rival jabs by Pfizer-BioNTech and Moderna, which have 95 percent and 94.5 percent rates respectively.
Hours earlier, on Monday afternoon, the health ministry launched an online platform for citizens to register for vaccinations, but it had not said the campaign would begin the next day and the page was not functional on Tuesday.
It has said health workers, security forces and the elderly would be prioritised and that the vaccine would be administered free of charge, but has given few other details.
The first jabs arrived as the Iraqi government faces growing criticism of its handling of the pandemic.
The country has been hit by a second wave of Covid-19 infections, with more than 3,000 new cases reported daily, a few months after they had dropped to around 700 a day, and deaths also tripling to around 25 a day in recent weeks.
To stop the spread, Iraq has imposed overnight curfews during weekdays and full lockdowns on Fridays, Saturdays and Sundays, with obligatory mask-wearing in public.
But there is little commitment by either the public or security forces deployed to enforce the measures, in a country whose health sector has been ravaged by decades of war, corruption and slim investment.
Some Iraqi officials have already been vaccinated.
Two current and one former Iraqi official told AFP in January they had already received doses of “the Chinese vaccine”.
They said 1,000 vaccine doses had been gifted to a senior Iraqi politician through contacts in China and had been distributed to top politicians and government officials.