Wood's change of heart follows suggestions that if he went back he should refund Australian taxpayers for the cost of the operation to free him out of the profits he will make from selling his story to a television station.
Wood, 63, a US-based engineering contractor who was freed last week after 47 days in captivity, suggested on his return to Australia on Monday that he might go back to Iraq to pursue contract work in reconstruction efforts.
Wood had "lost commercial opportunities during his incarceration", his brother Vernon said on Tuesday, but "he definitely won't be going back".
"Douglas at the first instance did say he would consider going back to Iraq, but later on he said, in deference to his family and other people and the efforts the Australian government had gone to, it would be irresponsible for him to go back," Vernon said.
Wood has been hailed as a hero since his return to Australia, but a sour note crept into the celebrations when it was revealed that he had sold his story to a television network for a sum put at $155,000 to $310,000.
Defence Minister Robert Hill said Wood would not be asked to contribute to the cost of his rescue operation, which involved sending a special Australian negotiating team to Baghdad.
He said it was "clearly a very expensive exercise", but that it was the government's responsibility to do everything possible to rescue an abducted Australian.
"Douglas at the first instance did say he would consider going back to Iraq, but later on he said ... it would be irresponsible for him to go back"
Douglas Wood's brother, Vernon
Any financial return Wood gained would be small compensation for his traumatic ordeal, Hill said.
There have been conflicting accounts of how Wood was freed, but the government says he was picked up in an operation by Iraqi and US troops.
Foreign Minister Alexander Downer has also said that, although "it is a free world", the Australian government would discourage Wood from returning, in line with standard advice to citizens to avoid the country.