He was captured at a safehouse in Pakistan with a top al-Qaeda member in 2002, and accused of taking part in a plan to bomb the US.
But the US Department of Defense said his detention was no longer considered necessary.
It said Algeria had given assurances that he would be treated humanely.
In a statement, the department added that US authorities recommended that Mr Barhoumi could be sent back to his native country “subject to security… assurance”.
“The United States appreciates the willingness of Algeria, and other partners to support ongoing US efforts toward a deliberate and thorough process focused on responsibly reducing the detainee population and ultimately closing of the Guantanamo Bay facility,” the statement said.
The department provided no further details about Mr Barhoumi.
Algeria has not publicly commented on the issue.
With the latest release, 37 detainees remain – including 18 eligible for transfer – at Guantanamo Bay, which is part of a US naval base complex in south-eastern Cuba.
Since 2002, the detention facility has been used to hold what the US describes as captured unlawful combatants during America’s war on terror.