"Compensation will be provided to both families," White House spokesman Josh Earnest said, adding that the final details had yet to be agreed.
US President Barack Obama expressed his profound regrets on Thursday to the families of Italian aid worker Giovanni Lo Porto and US contractor Warren Weinstein.
"We will identify the lessons that can be learned from this tragedy and any changes that should be made. We will do our utmost to ensure it is not repeated," Obama said.
The White House said on Thursday that a US operation in January against an Al Qaeda compound near the Afghan-Pakistan border killed the two hostages, along with an American member of the jihadist group.
Another American, Al-Qaeda spokesman Adam Gadahn, was killed, "likely in a separate US government counterterrorism operation."
"No words can fully express our regret over this terrible tragedy," the White House said, revealing the previously classified finding. The president "takes full responsibility for these operations."
Lo Porto disappeared in January 2012 in Pakistan.
Weinstein was snatched after gunmen tricked their way into his home in Lahore on August 13th 2011, shortly before he was due to return home after seven years working in Pakistan.
He later appeared in a video in which, under apparent coercion, he asked the United States to free Al-Qaeda prisoners.
"Analysis of all available information has led the intelligence community to judge with high confidence that the operation accidentally killed both hostages," the White House said.
"The operation targeted an Al Qaeda-associated compound, where we had no reason to believe either hostage was present, located in the border region of Afghanistan and Pakistan."
The White House statement did not identify which US agency carried out the operation, which suggests it was carried out by an intelligence service rather than a military unit.
"We have concluded that Ahmed Faruq, an American who was an Al Qaeda leader, was killed in the same operation that resulted in the deaths of Dr. Weinstein and Mr. Lo Porto," the White House said.
"We have also concluded that Adam Gadahn, an American who became a prominent member of Al-Qaeda, was killed in January, likely in a separate US government counter-terrorism operation," it added.
"While both Faruq and Gadahn were Al-Qaeda members, neither was specifically targeted, and we did not have information indicating their presence at the sites of these operations."