At least 12 people were injured in the attack on the Taji military camp, north of Baghdad.
US military sources said an American soldier, an American contractor and a British soldier were killed. No names have yet been released.
Tension has been high since the US killed senior Iranian commander Qasem Soleimani in a drone strike in January.
A retaliatory Iranian strike on al-Asad – another base hosting US troops – on 8 January left more than 100 soldiers suffering from traumatic brain injuries (TBI).
However, both Iran and the US appeared then to want to draw a line under the matter and there have been no major flare-ups since.
A statement from the US-led coalition in Iraq and Syria confirmed that 18 rockets had struck the base and three coalition personnel had been killed.
In an earlier tweet, a spokesman for the coalition said the attack happened at 19:35 local time (16:35 GMT) on Wednesday. He added that an investigation had been launched.
The UK Ministry of Defence said in a statement that the British soldier who was killed was a member of the Royal Army Medical Corps.
“The service person’s family have been informed and have requested a period of privacy before further details are released,” the statement…