Mr Bezos wrote in a tweet that the 500ft tall clock, which will cost £30million ($42million) to build, will be powered by Earth’s thermal cycles.
In a blog post he wrote: “It a special Clock, designed to be a symbol, an icon for long-term thinking.”
The clock has been in the works for 30 years and is designed to tick just once a year, according to the blog.
It has a “century hand” that moves forward once every hundred years and a cuckoo which comes out on the millennium.
The clock is not designed to keep track of seconds, minutes or hours, and will tick once a year for 10,000 years.
The post continues: “Building a Clock inside a remote mountain is a big task.
“Construction is under way and we’re making progress every day.”
The project was started by American inventor Danny Hillis, with Mr Bezos saying he has been helping out for “at least the last half dozen years”.
Mr Bezos is one of several financial backers of the 10,000 year clock, which is being built by the non-profit cultural institute the Long Now Foundation.
The institute has said the clock will sometimes play music using its bells.
Each time it plays a melody it will be one that it hasn’t played before.
The foundation said: “The Clock’s chimes have been programmed to not repeat themselves for 10,000 years.
“Most times the clock rings when a visitor has wound it, but the Clock hoards energy from a different source and occasionally it will ring itself when no one is around to hear it.”
The Long Now Foundation has not said when the project will be finished.
The clock will be opened to the public once completed.
Mr Bezos’s revelations come after it emerged that Amazon is working on its own Artificial Intelligence (AI) chipset to power the next-generation of Echo devices.
A custom Amazon chip would allow the smart speaker to better handle speech recognition by processing data locally – rather than sending everything to the cloud first.