On Wednesday, General Allen broke a long silence on the investigation, releasing a statement in Kabul through his spokesman, Maj. David Nevers. “From the outset, the general placed his faith in — and fully supported — the investigative process,” Major Nevers said. “He’s obviously pleased by the outcome.  But more critically, he is grateful for the support he received throughout this process from his chain of command, friends, family and colleagues.”

Late Tuesday, George Little, the Pentagon press secretary, released a statement confirming that Mr. Panetta had been officially informed that the inspector general closed the investigation into General Allen.

“The secretary was pleased to learn that allegations of professional misconduct were not substantiated by the investigation,” Mr. Little said. “The secretary has complete confidence in the continued leadership of General Allen, who is serving with distinction in Afghanistan.”

The inquiry was seen as a significant burden on General Allen as he ended his tenure in Afghanistan with the charge to begin drafting proposals for President Obama on how to draw down American forces there this year and end the combat mission by the end of 2014.

Although the exact content of the e-mails remains unknown, an official conclusion of no wrongdoing will no doubt be seen as a professional and personal exoneration for General Allen after an embarrassing period near the end of a highly respected Marine Corps career.

The F.B.I. discovered the e-mails during an investigation into anonymous e-mails to Ms. Kelley. Those messages, which warned her to stay away from Mr. Petraeus, had been sent by Paula Broadwell, Mr. Petraeus’s biographer. Mr. Petraeus admitted to having had an affair with Ms. Broadwell and resigned from the C.I.A. on Nov. 9. The F.B.I. sent the e-mails between General Allen and Ms. Kelley to the Pentagon on Nov. 11.

Like General Allen, Mr. Petraeus was a social acquaintance of Ms. Kelley’s when he was stationed at MacDill Air Force Base in Tampa, the headquarters of Central Command.

The inspector general’s finding, which was not wholly unexpected, was first reported Tuesday on the Web site of The Washington Post.

What remains unknown is the fate of General Allen’s nomination to become the top NATO commander, which was planned before the disclosure of the e-mails. He could be nominated to that position or to another senior post — or he could retire.

“The final decision has not yet been made on General Allen’s nomination,” one senior official said.

During the inquiry, about 15 investigators on the Pentagon inspector general’s staff focused on 60 to 70 e-mails that “bear a fair amount of scrutiny,” said one official who was briefed on the inquiry.

Pentagon officials had described the messages between General Allen and Ms. Kelley as potentially “inappropriate communication.” Law enforcement officials said the e-mails numbered in the hundreds and covered two and a half years starting in 2010, when General Allen was the deputy commander of Central Command.

The inspector general’s inquiry looked into whether the e-mails violated Defense Department policy, government regulations or military law. The questions included whether the e-mails contained inappropriate language that was on a government computer, whether they indicated an inappropriate relationship as defined under military law, whether they involved more than an incidental use of government property for personal matters and whether there were security breaches.

Gen. Joseph F. Dunford Jr. has been confirmed by the Senate to succeed General Allen as part of a standard rotation and is expected to take up the senior command position in Kabul in the coming weeks.