Nick Hall, 34, lost his balance as he helped the climbers into a Chinook helicopter, KING-TV in Seattle reported Friday.
The park service said Hall fell about 3,700 feet on the mountain's northeast side.
Hall was a four-year veteran of Mount Rainier National Park's climbing program and a native of Patten, Maine. He was unmarried.
Three of the hikers made it into the helicopter but inclement weather kept the fourth from being evacuated. That person spent Thursday night on the mountain with rescue personnel.
The park service said the four climbers are from Waco, Texas. Their names were to be released once their families had been notified.