Bombers have hit Iraqi security forces in and around Baghdad, killing at least 33 people in two separate attacks.
Wood has thanked his rescuers in a public statement
At least 25 Iraqi soldiers were killed in the first blast, by a suicide bomber wearing an Iraqi army uniform.
Hours later, a suicide car bomber slammed into a police patrol in southern Baghdad, killing eight.
The attacks come on the same day that Australian hostage Douglas Wood, 63, was freed after being held captive in Iraq for six weeks.
Mr Wood was freed during an Iraqi security operation, Australian Prime Minister John Howard said.
"He [Wood] was under a blanket. He was tied down and they [rebels] claimed that he was their father and he was sick," Iraqi General Nasir Abadi told a news conference in Baghdad.
"But when they [the troops] uncovered him they found him."
The former hostage has thanked his rescuers and is now undergoing medical tests.
The first of Wednesday's two explosions took place at a canteen inside an army base in the town of Khalis, 60km (40 miles) north of Baghdad.
Army officials say the attacker waited until soldiers had gathered for lunch before blowing himself up.
About 30 people are reported to have been injured in the blast.
The BBC's Caroline Hawley in Baghdad says the attack will be extremely worrying for Iraqi security forces.
It marks the second time in four days that a bomber in army uniform has infiltrated an Iraqi military base.
The last such attack was on Saturday, killing four people.
At least 900 people - mostly Iraqi civilians - have been killed in renewed violence since a new interim government was formed on 28 April.
The blast - described by an Iraqi army spokesman as "massive" - occurred at about 1300 local time (0900 GMT).
Iraqi officials said most of the injured were sent to hospitals in the nearby town of Baquba.
An investigation has been launched into the incident.
In the second attack, a suicide car bomber detonated explosives as police drove through Baghdad's Zafaranya neighbourhood.
At least 18 people were wounded in addition to the eight officers killed.