The attacks were carried out near Camp Speicher, 160 kilometers (100 miles) north of Baghdad in the Salaheddin province, according to claims on Twitter seen by SITE Intelligence Group.
ISIS said, using derogatory terms in reference to the Iraqi army and Shia sect, that a "gathering of the Safavid (Iraqi) army and its Rafidhi (Shia) militias," a barracks and a headquarters, all on the road connecting "Speicher Base/Fourth Division" were hit with a truck carrying six tons of explosives.
Each of the explosions resulted in the "complete destruction and elimination" of the target, it added.
Iraqi news websites said there were only two suicide bombings leaving two security forces dead and 13 wounded.
“Two car bombs driven by a French and a Qatari suicide bombers exploded today, targeting a security forces gathering on the highway that links between Speicher Base and the University of Tikrit, which resulted in killing two security forces elements and wounding 13 others,” a source told website Iraqi News, without mentioning the Syrian bomber.
Photos shared by ISIS showed smiling young men, each with their right index finger pointing upward in a gesture referring to the unity of God.
They were named as Abu al-Talha al-Firansi, the Frenchman; Abu Omar al-Qatari, from Qatar and Abu Ukasha al-Shami, from Syria.
Others photos showed what appeared to be explosions.
Camp Speicher, outside the city of Tikrit, was the scene of a June massacre in which nearly 1,700 soldiers died during an ISIS sweep in which the jihadist group seized large swathes of Iraq’s north and west.
Estimates about the number of ISIS members vary widely, although more conservative numbers used by the US government claim ISIS has between 20,000 and 35,000 fighters, some 3,400 of which are believed to be foreigners.
In January, French Interior Minister Bernard Cazeneuve said a total of 73 of his countrymen had died in "terrorist operations" in Iraq and neighboring Syria.
Large swathes of land in Iraq have become ISIS strongholds as the extremist group, which declared a "caliphate" in the territory it seized in Iraq and Syria, drove Iraq’s army — the recipient of $25 billion in US training and funding since the 2003 invasion — to collapse.
According to a report by the United Nations Assistance Mission for Iraq (UNAMI) earlier in February, fighting and other violence in Iraq killed at least 1,375 people including 790 civilians in January.
However, the UN numbers do not include territories held by ISIS.
The group has executed thousands in Iraq and Syria, targeting, in particular, ethnic and religious minorities.
The US-led anti-ISIS coalition has been bombing Iraq since September and has so far billed Iraq $260 million, despite failure to stop the advance of militants.
However, the air campaign, which Washington says aims to degrade ISIS’ military capability, remains the subject of debate, with critics pointing to ISIS’ advances and battlefield successes despite the raids.
The expansion of terrorist groups in Iraq raises questions about the effectiveness of the US anti-terrorism campaign since 2001.