It's all legal.
The average payment was about $59,000, but about 2,300 veterans, or 4 percent of the total, received concurrent payments of $100,000 or more, the Government Accountability Office said.
The highest payment was to a veteran who received $208,757 in combined payments in 2013.
Some lawmakers say the report shows the need for better coordination among government programs that are facing severe financial constraints. The Social Security Disability Insurance trust fund could run out of money in as soon as two years, government officials say.
"We should fulfill our promises to the men and women who serve, but we need to streamline these duplicative programs," said Sen. Tom Coburn, R-Okla., who requested the study.
Veterans groups disagree. They say the retirement money was earned for years of service in the military, while disability payments are compensation for service-related injuries and wounds.
In most cases, veterans who receive a combination of benefits are severely disabled. About 4 in 5 veterans who got triple payments had a disability rating of at least 50 percent, the GAO said. Nearly half of those receiving triple payments were at least 60 years old.
Louis Celli Jr., a Washington representative for the American Legion, said critics of the multiple benefits are "misguided and uninformed." He said the report "should simply be filed in the category of one of Sen. Coburn's parting shots to loyal upstanding American patriots who have sacrificed so much for this country."
Coburn, a longtime critic of government spending, is retiring at the end of the year. He said in an interview that the report raises legitimate questions about whether disability benefits are getting to those who truly need them.
"This is billions of dollars a year in duplicative payments," Coburn said. "We ought to reassess and say, 'Are we doing more than take care of people in need?' I'm not against the military. I don't think they should be triple dipping."
Most Americans would find it hard to understand how someone making $86,000 a year in tax-exempt VA income qualifies for Social Security Disability Insurance, when civilian workers are disqualified from the program if they make as little as $13,000 a year, Coburn said.
Only 17 percent of those who received multiple forms of compensation had suffered a combat-related disability, according to the GAO.
Veterans have long been exempted from rules that deny Social Security benefits to anyone with other income exceeding $13,000 a year.
But until the Sept. 11, 2001, terrorist attacks, veterans were barred from receiving both military retirement pay and Department of Veterans Affairs' disability benefits. Under a Civil War-era statute, the Pentagon docked retirement pay dollar-for-dollar up to the amount of disability benefits from the VA.
With bipartisan support, Congress changed that law in 2002, gradually restoring military retirement pay to veterans also drawing disability benefits from the VA.
"Our nation's status as the world's only superpower is largely due to the sacrifices our veterans made in the last century," Sen. Harry Reid, D-Nev., said in March 2002 when the bill was being debated.
"Rather than honoring their commitment and bravery by fulfilling our obligations, the federal government has chosen to perpetuate this longstanding injustice," Reid said. "Quite simply, this is disgraceful and we must correct it."
At the time, then-Sen. John Warner, R-Va., a former Navy secretary, posed a question to fellow senators: "How can we ask the men and women who have so faithfully served to sacrifice a portion of their retirement because they are also receiving compensation for an injury suffered while serving their country?"
Warner acknowledged that the change would have "significant cost," but added; "Is the cost too high? I think not."
About 3 percent of the nation's 1.9 million military retirees collect all three benefits, the GAO said.
The report did not recommend changes to the program. The VA said in a response that it "generally agrees" with the report's conclusions. Social Security officials did not comment.