Edwards, 25, will be committed to Central Regional Hospital in Butner.
The N&O said the ruling came after experts determined that he had schizoaffective disorder, which caused delusions and hallucinations.
Edwards was charged with six felonies, including malicious use of incendiary device.
He was accused of setting fire to a backpack and guitar beside the tree on Nov. 2, 2017.
After the fire ignited, Edwards walked away. Moments later, UNC Physics and astronomy professor Dan Reichart saw the flames and tried to put them out.
Warning: This video may be graphic for some
However, a fuel canister in the backpack exploded, resulting in the loss of 10-11 percent of skin on Reichart's face, lower arms, and back of his hands.
"I was an Eagle Scout as a kid, so I've had lots of experience with fires, and I didn't think this one was too big to kick out," Reichart told ABC11. "I tried but it grew very quickly, and then it exploded -- I would never have approached it had I suspected there was an explosive device in there."
Reichart was released from the hospital days after the explosion.
During the trial, defense's forensic evaluation concluded that Edwards "was incapable of distinguishing right and wrong in a reality-based fashion due to the effects of psychosis," the N&O reported.
The Davie Poplar tree marks the spot where, as legend has it, Revolutionary War General William R. Davie selected the site for the University.
The tree has been struck by lightning and survived several hurricanes, school officials said.
Officials estimate the tree sustained at least $100 worth of damage, but school officials said the damages are superficial.