The Real IRA (Irish Republican Army), a dissident republican group aiming to end British rule in the province, said it carried out the shooting at the barracks.
Cengiz Azimkar and Mark Quinsey of the Royal Engineers were shot dead as they collected a pizza delivery outside the Massereene base.
Two other soldiers and two delivery staff were injured.
The attack on the base was followed by the killing of a police officer, which was claimed by the Continuity IRA, another group that split from the IRA after a ceasefire was agreed with the British government in 1997.
Police are questioning three other men over that killing.
Thousands of people attended the funeral of Constable Stephen Carroll on Friday.
Politicians from both the republican and unionist - supporters of British rule - camps have condemned the attacks and vowed to continue to work together in the province's government.
The two sides agreed to share power in 2007 with Sinn Fein, a republican group with strong links to the IRA, joining the Democratic Unionists in government.