"I received a call a month ago from my boss in the [Baath] party, Sattam Farhan, in Syria, to do an operation to destabilise the regime," Mr Ibrahim said in the broadcast confession.
Many Baathist officials fled to Syria soon after the collapse of Saddam Hussein's regime, following the US-led invasion in March 2003.
Mr Ibrahim said his organisation had paid $10,000 (£6,000) to a facilitator who knew the security arrangements on the roads from Muqtadiya in Diyala province, north-east of Baghdad.
Mr Ibrahim was claiming responsibility for the bombings at the Iraqi finance and foreign ministries.
Surveillance video widely broadcast on Iraqi television stations showed a truck carrying three large red water tanks, in which the explosives were hidden, approach the gate in front of the foreign ministry, near the heavily-protected Green Zone.
A refrigerated truck was used in the finance ministry attack.
On Saturday, Iraqi Foreign Minister Hoshyar Zebari said the militants must have been helped to get through checkpoints to foreign and finance ministry buildings in the city centre.
Nouri al-Maliki tours the bomb site at the Foreign Ministry
Mr Zebari also warned violence may rise in the coming days, six weeks after US troops withdrew from Iraqi cities.
"According to our information, there has even been collaboration between security officers and the murderers," Mr Zebari told reporters on Saturday.
He said the attacks had been well planned, and asked how the trucks had been allowed into central Baghdad - a no-go area for heavy vehicles.
The authorities have detained 11 security officers on suspicion of negligence following the blasts.
Correspondents say the attacks raise concerns about the ability of Iraqi authorities to ensure security after taking over responsibility for protecting urban areas at the end of June.
Though violence in Iraq has declined since the peaks of 2006 and 2007, it continues to be the target of frequent bomb attacks.
Iraqi Prime Minister Nouri Maliki has blamed the recent attacks on al-Qaeda in Iraq, and supporters of Saddam Hussein.
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