"We have been advised he has passed away," said Mary deTracy, a medical investigator with the medical examiner's office here.
Peter Cooley, 39, of Cape Elizabeth, Maine, had been rescued several hours earlier from the 12,300-foot level of the 14,410-foot mountain southeast of here.
An Oregon Army National Guard Chinook helicopter that had been standing by in Yakima, about 100 miles away, swept in when the clouds parted briefly and winched the injured climber aboard after he was strapped to a litter.
Cooley was taken to Madigan Army Medical Center near Tacoma, said Dave Kuhns, a Fort Lewis Army base spokesman.
"He was deceased when the helicopter arrived at Madigan," Kuhns said Monday night, relaying information he received from Madigan officials.
Cooley fell 30 feet early Saturday on Liberty Ridge - one of the most difficult routes up the mountain. His climbing partner, Scott Richards, 42, also of Cape Elizabeth, was able to reach him, set up a tent and call for help on a cell phone.
Cooley had been reported in stable condition Monday afternoon but had symptoms of a serious head injury and also appeared to have some sort of shoulder and leg injuries. Awaiting rescue, he was incoherent and agitated as he drifted in and out of consciousness.
Earlier Monday, two national park rangers reached the climber and his companion by foot but park officials said then it did not appear rescue was likely until Tuesday, due to the steep terrain and adverse weather conditions.
"It looked like this morning the weather was going to stay bad for days and we were prepared to implement this rescue without the use of helicopters," park spokeswoman Lee Taylor told KOMO-TV shortly after the helicopter rescue.
The two climbing rangers who reached Cooley earlier Monday had him "all set up in a litter and ready to go so when the helicopter got there they could hook up the cables and lift him up into the copter," Taylor added.
Richards and the rangers are expected to spend the night on the mountain.
A helicopter had dropped supplies to the two climbers Sunday night. The supplies included a radio, food, water, warm clothing and sleeping bags.
The two men were stranded on a 45-degree slope with steep and rocky terrain above and below them.
"There couldn't be a worse place on the mountain to try to do a rescue; it's very extreme terrain," said park spokeswoman Lee Taylor.
Cooley and Richards are described as experienced climbers who had scaled Mount Rainier before. In 2001, they tried to climb Liberty Ridge, but bad weather forced them to take an easier route.
Cooley once worked on a search-and-rescue team on Mount McKinley in Alaska and climbed that mountain solo. This was his fourth ascent of Mount Rainier.
Cooley's aunt, Kristi Witker, of New York City, earlier described him as "an excellent mountain climber" but added that "in my last conversation with him, I said, 'Please give up mountain climbing. You're just getting to that point where you've been so lucky and nothing's ever happened, but luck runs out.' "
Richards has climbed Mount Blanc and Mount Chamonix in the Alps.