The environmental organisation encased activists in five heavy containers which were manoeuvred into place during the night.
Abseilers also set about installing letters spelling out "Climate emergency" on the building's windows.
The protest comes ahead of BP's annual general meeting in Aberdeen, Scotland, on Tuesday.
Greenpeace wants BP to switch to purely renewable energy or close its operations.
"We're shutting down BP's HQ because business as usual is just not an option," said container occupant Paul Morozzo.
"BP is fuelling a climate emergency that threatens millions of lives and the future of the living world.
"We must stop searching for new oil and gas if we want a liveable planet. BP must clean up or clear out."
Six abseilers could be seen on the outside of the building in plush St. James's Square, while a couple of activists sat on top of the two containers outside the the main doors.
The containers are decorated with a brick effect covering and photographs. The boxes have food, drink, toilets, lights, books and games inside.
- 'No future in oil' -
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"We welcome discussion, debate, even peaceful protest on the important matter of how we must all work together to address the climate challenge," a BP spokeswoman told AFP.
"But impeding safe entry and exit from an office building in this way is dangerous and clearly a matter for the police to resolve as swiftly as possible."
A police spokesman said no arrests had been made. Parts of the square were screened off with police tape and a handful of officers patrolled the cordon.
The stunt comes a month after the Extinction Rebellion climate protests brought parts of central London to a halt.
"We're seeing it as part of the same wave of campaigning and activism right now because people are very concerned about the climate emergency," Greenpeace campaigner Morten Thaysen told AFP at the police cordon.
"There isn't a future in oil. The company has two choices: to go 100 percent renewable or to start winding down the business. All the oil companies need to go in this direction," Thaysen said.
"We don't have the luxury to wait around for them to make these decisions by themselves. The transition needs to start now."