The body of Wheeler, 66, was discovered on New Year's Eve as a garbage truck emptied its contents at the Cherry Island landfill. His death has been ruled a homicide.
Wheeler retired from the military in 1971 and lived in New Castle. He reportedly was last seen Dec. 28, traveling on an Amtrak train from Washington to Wilmington.
Police have determined that all the stops made Friday by the garbage truck before it arrived at the landfill involved large commercial disposal bins in Newark, several miles from Wheeler's home.
"He was just not the sort of person who would wind up in a landfill," said Bayard Marin, an attorney who was representing Wheeler in a dispute over a couple's plans to build a new home in the historic district of Old New Castle where Wheeler lived.
Wheeler, the son of a decorated Army officer, was a graduate of the U.S. Military Academy and a veteran of the Vietnam war. He was the first chairman of the Vietnam Veterans Memorial Fund, and led the multimillion-dollar fundraising effort to create the memorial on Washington's National Mall.
Fund founder and president Jan Scruggs said Wheeler dedicated himself to ensuring that service members were given the respect they deserve.
"I know how passionate he was about honoring all who serve their nation, and especially those who made the ultimate sacrifice," Scruggs said in a statement released Monday.
Wheeler served in the administrations of Presidents Ronald Reagan and George H.W. Bush.
In addition to chairing the memorial fund, Wheeler served as a special assistant to the secretary of the Air Force. He also was the first chief executive of Mothers Against Drunk Driving.
Wheeler's military career included serving in the office of the secretary of defense and writing a manual on the effectiveness of biological and chemical weapons, which recommended that the United States not use biological weapons.
"He was a very humble kind of guy, actually," Marin said. "He was never the kind of person who would talk about all the wonderful things he did in his life."