CNN said officials have not named the victim or said where he was found, but an officer in the Oregon National Guard confirmed the climber was found in a snow cave.
Earlier, there was optimism as rescuers announced they had spotted the snow cave and thought it might help them find the men.
Teams of handpicked rescuers began climbing Mount Hood before dawn in a decisive "push" to find the three climbers, who have been missing for a week.
The three missing climbers -- Kelly James, 48, Brian Hall, 37, and Jerry "Nikko" Cooke, 36 -- became trapped on the more treacherous north slope of the mountain Dec. 9.
James called family members from his cell phone Dec. 10 to report he had taken refuge in a snow cave while his companions headed down the mountain for help.
James and Hall are from Dallas and Cooke is from New York.