Tommy Caldwell and Kevin Jorgeson became the first free climbers to scale the sheer Dawn Wall of the El Capitan rock formation in California.
They are the first climbers to do so without the usual aids, relying sometimes on fingertip grips.
Jorgeson said it should show people the importance of teamwork and persistence.
He said the experience "recalibrates your perception of what you can do and what's possible. Now that we've done this, who knows what comes."
His fellow record-breaker Caldwell told the New York Times: "I would love for this to open people's minds to what an amazing sport this is."
Both men said they had been touched by the number of people who had been inspired by their achievement.
The task began on 27 December and while scaling the 3,000ft (914m) rock, they had even climbed in darkness, when sweat was less of an issue.
They took rest days to wait for their finger cuts and grazes to heal and used tape and even superglue to speed up the process.
Caldwell said support climbers had provided them with fresh fruit and vegetables every five days, plus they had burritos, chocolate and even coffee.
In spare moments, he said, he read the autobiography of legendary climber Barry Blanchard.
Jorgeson said the Dawn Wall "personifies dreaming big and making it happen".
He added: "It's just a super-concrete example and an iconic, beautiful place with amazing images and a great story of perseverance and teamwork and making it."
How do they do it?
How do you climb a smooth rock face?
The two American climbers who spent 19 days clinging to a vertical rock face say they hope their achievement will inspire others.