Munn's plane was lost on a remote glacier in Kings Canyon National Park during a training flight 65 years ago. All four crewmen were lost; only one other body has been found.
Jeanne Pyle, Munn's younger sister, said Army officials from Virginia contacted the family Friday to inform them about the airman's identity.
The military asked to meet with the family about arranging a funeral or memorial service, family members said.
Pyle said the family would like Munn's body to be buried in the family's cemetery near St. Clairsville, Ohio, Munn's hometown.
"This will be a closure for us," said Pyle, 87.
Munn's identity will take a couple more weeks to confirm, said Shari Lawrence, a public affairs officer for the Army's Human Resources Command in Alexandria, Va.
"We know who we believe it to be," Lawrence said.
Munn's body was found in August by Seattle-based author Peter Stekel and his hiking partner. Stekel was in the Sierra doing research for his book "Final Flight" on the crash that killed Munn and three others.
Stekel said Tuesday that when he found the body on the glacier last year and viewed pictures of the men, he was fairly confident Munn was the man he had found.
Stekel described what he found to the family members, including Munn's "wavy blond hair."
Pyle said Munn, who was Glenn to his family, was smitten with flying: "He talked about it all the time. He loved it."
Munn, 23, was on board an AT-7 training plane when it was knocked off course by bad weather in November 1942 and crashed on the Mount Mendel glacier.
The plane was supposed to be flying between Mather Field, near Sacramento, and Los Banos, Stekel said.
Also on board the flight were Leo Mustonen, 22, of Brainerd, Minn.; William Gamber, 23, of Fayette, Ohio; and John Mortenson, 25, of Moscow, Idaho.
Munn's youngest sister, Lois Shriver of Emsworth, Pa., still recalls hearing about her brother's missing plane for the first time.
She was away from home in Zanesville, Ohio, training for a gas station attendant's job. Her parents had not told her. But the story of the missing plane was in a local newspaper.
"A fellow walked into an office I was in and said, 'Is that Munn boy any relation to you?' " she said. "We naturally thought he was going to be found because at the time they said he was missing."
Mortenson's dog tags were found in 1947 by a pair of Sierra Club hikers on a backpacking trip. But no other trace was found of the four airmen.
Over the years, the sisters remembered Munn on his birthday, Jan. 18, but gradually put the loss of their older brother behind them.
Then, in 2005, ice climbers found an airman's body near the 13,710-foot Mount Mendel.
That discovery, said Shriver, revived the family's sorrow. The family hoped the body was Munn's.
It was eventually identified as Mustonen's.
"After the first time, when it wasn't him, it was a big disappointment," Shriver said. "Before that we had kind of let it go, but we didn't forget."
She added: "I just missed him terribly."
