A defense official and a senior U.S. official said the Marine Corps general had been cleared of any wrongdoing. The officials spoke on condition of anonymity because the decision had not been announced publicly.
The matter was referred to the Pentagon in November by the FBI during the course of its investigation of emails between Petraeus and his biographer-turned-paramour, Paula Broadwell. The FBI turned up thousands of emails between Allen and Jill Kelley, who was said to have received threatening emails from Broadwell.
At the time, officials said 20,000 to 30,000 pages of emails and other documents from Allen's communications with Kelley between 2010 and 2012 were in question.
Shortly after being contacted by the FBI, Defense Secretary Leon Panetta referred the matter to the Pentagon's inspector general, while expressing confidence in Allen and deciding that he would remain in Kabul as commander of all allied forces in Afghanistan.
At the same time, Allen's nomination to be the next U.S. commander of NATO forces in Europe was put on hold. The officials said Tuesday the White House had not decided whether to go forward with the nomination.
Allen's successor in Kabul, Marine Gen. Joseph Dunford, has been confirmed by the Senate and is scheduled to take over on Feb. 10.
Allen had maintained he did nothing wrong in the Kelley communications, but he has not spoken publicly about the specifics of his email exchanges with her. She served as a sort of social ambassador for U.S. Central Command in Tampa, Fla.
Petraeus is a former Central Command commander, and Allen is a former deputy commander there.