The man was recorded near the pinnacle of the 95-storey skyscraper around 6.30am this morning.
Cops say he is now inside the building and talking with officers.
The structure is the tallest building in the UK.
One eyewitness tweeted: “At least one person climbing up the outside of the Shard in central London.
“Two police cars, two ambulances and a drone on the scene.”
Another said: “There’s a person climbing up The Shard!
“Police darting around London Bridge station. Saw a drone near the top too. Not sure who that belongs to.”
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