Private Pita Tukatukawaqa, 27, was the driver of a Warrior armoured car which was hit by a roadside bomb on Monday near the Black Watch regiment's new base just southwest of Baghdad.
He was the fourth soldier from the regiment killed since an 850-strong British battle group recently relieved US troops at Camp Dogwood, a base near the town of Mahmudiya.
According to the Fijian Embassy in London, more than 2000 Fijians currently serve with the British military around the world. A ministry spokesman said the bomb had been left by the road near Camp Dogwood on Monday.
The Black Watch regiment was recently redeployed to a US-run sector south of Baghdad ahead at the request of US commanders ahead of an assault on Falluja.
Camp Dogwood where the Black Watch is based lies west of the town of Mahmudiya, 20km south of Baghdad.
Britain, which has 8500 troops in southern Iraq, has moved 650 troops close to the Iraqi capital.
Seventy-four British troops have now died in Iraq since the US-led invasion in March 2003.