The new series, currently under the working title Snow, will follow Harington's popular character from the main eight-season fantasy epic.
Writing about the project on his blog, Martin said: “Yes, there is a Jon Snow show in development.”
Also in the post, he revealed the idea for the spinoff was originally suggested to him by 35-year-old British actor Harington.
He wrote: “Yes, it was Kit Harington who brought the idea to us.
“I cannot tell you the names of the writers/ showrunners, since that has not been cleared for release yet … but Kit brought them in too, his own team, and they are terrific.”
Jon Snow featured in Game Of Thrones as the illegitimate son of the Stark family and his journey included discovering that he was actually descended from the Targaryen family.
Harington was nominated twice for Emmy Awards for his portrayal of the character, and starred alongside his wife Rose Leslie, who played his lover Ygritte in the series.
Martin added: “There’s not much more I can tell you, not until HBO gives me a green light.”
He continued: “Various rumours are floating around about my involvement, or lack of same.
“I am involved, just as I am with The Hedge Knight and The Sea Snake and Ten Thousand Ships, and all the animated shows.
“Kit’s team have visited me here in Santa Fe and worked with me and my own team of brilliant, talented writer/consultants to hammer out the show.”
Game Of Thrones fans can also continue to follow the fantasy world through prequel series House Of The Dragon, which follows the rise of House Targaryen and takes place 200 years before the events of the main series.
The 10-episode HBO series stars Matt Smith as Daemon Targaryen and is based on Martin’s Fire And Blood novel.
Watch: Emilia Clarke confirms Kit Harington's Game Of Thrones series is happening