"For the last 100 years or thereabouts, we have been working on a thing called Everyday Life," said the band in the typewritten message.
It will be a double album, split into two halves, called Sunrise and Sunset, and released on 22 November.
The letter was signed by all four members of the band - but the recipient initially thought it was a hoax.
"Fake alert!" said Lena Tayara on Twitter, alongside a picture of the gold-embossed card. "Got this in the post this morning... Can't see why anybody would send it."
After fans reassured her it looked authentic, she changed her mind, writing: "If I'd known that card was genuine I would have put on a nicer tablecloth before I took the pics.
"But thanks for the card - I'm AMAZED and very touched."
Coldplay are the biggest-selling British band of the 21st Century. According to the Official Charts Company, they have three of the top 20 best-selling albums of the Millennium, led by 2002's A Rush Of Blood To The Head.
Their last record, A Head Full Of Dreams, was an uplifting, multicoloured dalliance with pop that saw the band collaborate with Beyonce, Stargate and Swedish pop maverick Tove Lo. It sold more than 2 million copies, and spawned 122-date world tour that grossed $523m (£402m) at the box office.
It was followed up by a companion EP, Kaleidoscope, and a side project with Pharrell Williams under the name Los Unidades, but the band have largely been silent since 2017.