The Swansea Building Society shared on social media that the postcard arrived at its Cradock Street address in Swansea along with the rest of the mail on Friday.
The postcard was addressed to Lydia Davis, whom employees speculated might have lived at the address when it was a house rather than a bank.
"The address is correct, we are still 11 (and 12) Cradock Street, but it's 121 years later than expected," Henry Darby, the bank's marketing and communications officer, told Wales Online. "It's wild, actually. A little bit spooky. The stamp itself is King Edward, so he was King from 1901 until 1910, and you could tell straight away from the handwriting and the way it speaks, 'Dearest, I could not', it was very much of the time."
Darby said much of the postcard is unreadable now, but the postmark appears to bear the date Aug 3, 1903.
A spokeswoman for the Royal Mail said the story behind the postcard's late arrival is unclear.
"It is likely that this postcard was put back into our system rather than being lost in the post for over a century. When an item is in our system, we are under obligation to deliver it to the correct address," she said.
-- BERNAMA