"They were found together in a pool," Cooper said. "We found their backpacks yesterday [Monday] and located them this afternoon."
Cooper did not know how the men died but suspected it was from hypothermia or drowning.
The bodies were flown by a Utah Department of Public Safety helicopter to Escalante, where they were identified by relatives, then sent to the medical examiner's office in Salt Lake City for autopsies.
Cooper described the rugged area as grooved with canyons up to 300 feet deep and anywhere from 16 inches to 600 feet wide.
To navigate the canyon, the men were required to execute a series of rappels and swim through pools of water that are cold and exceptionally high this year. The men were equipped with wet suits and ropes.
Bureau of Land Management employees and the volunteer fire department from the town of Tropic helped in search efforts.
The area is adjacent to Grand Staircase-Escalante National Monument, where the pair began their journey Wednesday at the Egypt trailhead, 26 miles south of State Route 12 off the Hole-in-the-Rock Road.
The search began after Underwood and Anderson failed to return at their designated time Saturday and family members contacted the sheriff's office.
As the search was under way Tuesday, family members from around Utah gathered at the trailhead.
Also on hand were Underwood's bishop and stake president with The Church of Jesus Christ of Latter-day Saints.
Stake President Larry Johnson said Underwood was married in August and was expected to graduate from the LDS-run university on Friday with a degree in physics.
Underwood was also a cadet in the school's Air Force ROTC program and was expected to receive a commission on graduation, Johnson said.
"He was one of the most well-rounded people I know," said classmate David Cullen, who recalled Underwood's positive attitude and can-do spirit.
Underwood's brother-in-law, Michael Hoffman, traveled to Escalante from Layton to take part in the vigil.
He described Underwood as an experienced rock climber who had had his share of spills.
"But nothing like this," Hoffman said.
Several of Anderson's cousins were also on hand Tuesday.
Jason Despain, one of the cousins who had traveled to the trailhead from Riverton, described Anderson as thoughtful of others.
"He also had a great laugh and was afraid of firecrackers," Despain said. "He was in great shape and could climb where most people can't."
Anderson was a student in BYU's construction management program and was also scheduled to graduate Friday, said program chairman J.P. Christopherson.
"He was known by most of the students as 'Peaches,' " Christopherson recalled. He said Anderson was active in the development of the department's Web site and was well known by the 400 members of the department's student organization.
The loss of the men will be felt deeply by the BYU student population, said the school's media relations director, Carri Jenkins.
Before the bodies were discovered, a group of seven people from Bozeman, Mont., hiked out of the same area Tuesday afternoon, a couple of days later than planned.
Perry Fishbaugh, the leader of the group, which ranged in age from 17 to early 20s, did not expect the water to be as deep or as cold as it was.
They started their trek Saturday.
"By the end of the day [Sunday] we were shivering but had plenty of food and water," Fishbaugh said. "We found some shelter, started a fire and spent the night." Many of the canyons, he said, were clogged with logs and other floating debris.