Ratchet was loaded onto a charter flight, which took off Sunday night for Kuwait. He's due in Minnesota later this week.
It was the third try by Operation Baghdad Pups to get Ratchet out of the country on behalf of Beberg, who says she couldn't have made it through her 13-month deployment without the affectionate mutt.
She and another soldier rescued the puppy from a burning pile of trash in May.
Beberg's quest to get the dog has gained international attention. More than 65,000 people from Illinois to Italy have signed an online petition urging the Army to let the puppy go to the United States.
The U.S. military has said the dog was free to leave but American troops could not be responsible for its transportation.
"We're happy the SPCA has made arrangements for his safe travel to the U.S., we hope he has a long, happy, fruitful life there," military spokesman Lt. Col. Paul Swiergosz said.
Beberg initially tried to send him with a military convoy from her base south of Baghdad to the airport for an Oct. 1 pickup. But the playful black dog with a touch of white on his nose, chest and paws was reportedly confiscated by an Army officer and sent back.
Baghdad Pups, a U.S. rescue program run by the Society for the Prevention of Cruelty to Animals International, tried again on Wednesday but was unable to get Ratchet to the flight, which took off with six other dogs instead.
On Sunday, a private security firm collected Ratchet from the small base, put him into a pet carrier and transported him to the airport on Baghdad's western outskirts.
Baghdad Pups coordinator Terri Crisp then took custody and boarded him on the charter. The effort will cost an estimated $5,000, according to the SPCA.
Beberg has been transferred to another military base to prepare for her departure from Iraq next month.
Her mother said bonding with the 6-month-old puppy was a life-saver for her daughter.
"He has been her emotional support, confidante, sanity-saver and a connection with something other than a war zone," Patricia Beberg said Sunday in a telephone interview.
She also urged the U.S. military to reconsider its policy that bars troops from caring for pets while on duty or taking them home.
"The animals are doing so much good for our soldiers, not only when they're there but when they come home," she said. "The military says it's very concerned about their mental health ... this is one way to help and it certainly doesn't cost as much as years and years of therapy."
Baghdad Pups has brought 56 dogs and six cats to the U.S. to be with their owners since February. The group says it is both rescuing animals who face abuse in Iraq, as well as helping soldiers who benefit from the bond developed with the animals.
The U.S. military cited several reasons for its pets policy, including health issues and difficulties in caring for the animals.
In June, a dog brought back to the U.S. by Operation Baghdad Pups tested positive for rabies after it was euthanized for other health problems. SPCA International spokeswoman Stephanie Scroggs said one cat also had to be put down.
On the Web:
Baghdad Pups site: http://www.baghdadpups.com