DeMuth, 42, died while trying to stop Rodgers during a high-speed chase that began in Wake County and ended in Nash County on September 8, 2012.
As part of the plea agreement, Rodgers is expected to spend about 35 years behind bars. He made an emotional statement in court to DeMuth's wife.
"I look upon your husband as one of my heroes, because he so unselfishly gave his life, and mine was spared. I can't tell you why," he said.
He also made a request.
"That you will someday, somehow forgive me for the things that I have done. I in no way, form or fashion, intended for any of this to happen," he said.
DeMuth's wife said in a statement Monday that she is pleased with the plea agreement, and thanked prosecutors, but said she will never truly have closure.
"There is no way to fill the enormous void that Gene's death leaves in our family. We will always long for his infectious smile, outgoing personality, love, and compassion. Our hearts are forever broken by his death, just as our lives are forever blessed by his life," said Michelle DeMuth.
Trooper DeMuth served with the North Carolina Highway Patrol for 12 years and was assigned to the Rocky Mount, Troop C District 1, Highway Patrol Office. He served his country as a United States Marine from 1988 to 1992. He began his law enforcement career in 1994 as a deputy with the Wilson County Sheriff's Office until moving over to the Edgecombe County Sheriff's Office.