The activist, in a blonde wig, shirt, jacket and tie, unfurled two flags from the tower, one reading “Citizens Assembly” and the other, bearing the Extinction Rebellion logo over an LGBT+ flag, reading “No Pride on a dead planet”.
Identified by the group as Ben Atkinson, a tree surgeon, he was arrested after evading police by unclipping his harness and sitting on a girder.
The group said he was made a ”free solo climb” and hung the banners ”to highlight government inaction on the climate and ecological emergency”.
As he climbed, police shouted for him to come down, and men in high-vis jackets called out to him from a nearby platform.
After evading officers for three hours, Mr Atkinson was taken into custody on suspicion of trespass on a protected site, the Met Police said. The offence carries a maximum sentence of 51 weeks' imprisonment or an unlimited fine.
The tower is currently under maintenance and surrounded by scaffolding.
He carried out the daring stunt just hours after appearing before London magistrates on charges relating to his climbing a lamppost at Marble Arch last spring.
But a charge of obstructing a constable and a charge of being a public assembly participant failing to comply with a condition were dropped, according to an Extinction Rebellion member who said she spoke for Mr Atkinson.
Katherine Beaumont said he had been demanding to speak to Mr Johnson "wig to wig", and accused the prime minister of "hiding from imminent global disaster".
After reaching the top, Mr Atkinson, from Cumbria, posted on Facebook a plea to Mr Johnson to "do something that could last for centuries".
Extinction Rebellion London’s Twitter account stated: “This rebel is desperate. The government is not listening, not telling the truth, not acting to protect us in the face of calamity. He faces terrorism charges. He faces jail."
Activists also staged a protest to Downing Street and blocked roads in central London on the penultimate day of a fortnight of demonstrations.
They brought traffic to a standstill with a large bamboo teepee at Oxford Circus in London’s West End as part of an “autumn uprising” campaign.
The protesters, joined by celebrities including Steve Coogan, defied a police ban on protesting in London.
Members staged sit-ins outside the Treasury and the entrance to Downing Street, ahead of the planned end of the action on Saturday at 6pm.