Americans claw their way to the top of Yosemite’s Dawn Wall to fulfil a five-year dream.

Two Americans yesterday completed what has long been considered the world's most difficult rock climb, using only their hands and feet to conquer a 900m vertical wall on El Capitan, the forbidding granite face in Yosemite National Park that has beckoned adventurers for decades.

Tommy Caldwell and Kevin Jorgeson became the first to "free-climb" the Dawn Wall, a feat that many had considered impossible. They used ropes and safety harnesses to catch them in case of a fall, but relied on their own strength and dexterity to ascend by grasping cracks as thin as razor blades and as small as coins.

The effort took weeks, and the two dealt with repeated falls and injuries. But their success completes a years-long dream that bordered on obsession.

Caldwell finished the climb first, and Jorgeson finished minutes later. The two embraced before Jorgeson pumped his arms in the air and clapped his hands above his head. They then sat down for a few minutes, gathered their gear, changed their clothes and hiked to the summit.

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The trek up the world's largest granite monolith began on December 27. Caldwell and Jorgeson ate and slept in tents fastened to the rock high above the ground and battled painful cuts to their fingertips much of the way.

Free-climbers do not pull themselves up with cables or use chisels to carve out handholds. Instead, they wedge their fingertips and feet into tiny crevices or grip sharp, thin projections of rock. In photographs, the two appeared at times like Spider-Man, splayed across the pale rock that has been described as being as smooth as a bedroom wall.

Both men needed to take rest days to wait for their skin to heal. They used tape and even superglue to help with the process. At one point, Caldwell set an alarm to wake him every few hours to apply a special lotion to his throbbing hands.

They also took physical punishment when their grip would slip, with long, swinging falls that left them bouncing off the rock face. The tumbles ended in startling jolts from their safety ropes.

Caldwell and Jorgeson had help from a team of supporters who brought food and supplies.

The 36-year-old Caldwell and 30-year-old Jorgeson ate canned peaches and occasionally sipped whisky. They watched their urine evaporate into thin, dry air and handed toilet sacks, called "wag bags", to helpers who disposed of them.

There are about 100 routes up the rock known among climbers as "El Cap", and many have made it to the top, the first in 1958. Even the Dawn Wall had been scaled.

No one, however, had made it to the summit in one continuous free-climb, until now.

"He doesn't understand the magnitude of the accomplishment and the excitement generated," said Mike Caldwell, Tommy's father, who along with 200 people gathered in a meadow below broke into cheers when the men reached the top.

The pioneering ascent follows five years of training and failed attempts for both Caldwell and Jorgeson. They got only about a third of the way up in 2010, when they were turned back by storms. A year later, Jorgeson fell and broke an ankle in another attempt.

Jorgeson has an impressive list of climbs in the United States, Europe and South Africa and works as a climbing instructor.

John Long, the first person to climb El Capitan in one day, in 1975, said recently of Caldwell and Jorgeson's free-climb that it was almost "inconceivable that anyone could do something that continuously difficult".

Family life in high places

Standing at the foot of a sheer cliff face as her husband clung on by his fingertips nearly 900m above, Becca Caldwell looked remarkably unperturbed.

"The fact he is up there is awesome for me," she said, squinting up at the small dot that was Tommy Caldwell.

"That's Tommy, he's kind of obsessed with mountains," said Mrs Caldwell, clutching their 21-month-old son Fitz. "I don't get worried or scared because I know he's safe on the wall - this is every day in our family life."

She said she would be at the summit to greet the two men.

It would be a special moment for the Caldwells because El Capitan is where their romance started.

"Tommy brought me here when we were friends, and we realised it was something special," said Mrs Caldwell, who is also a climber.

-AP / Telegraph Group Ltd