The 26-year-old, who joined the Shakers last summer, has made a strong start to the season and the club were keen to secure his long-term future.
The club have the option of extending Jones' contract by a further year when his deal comes to an end.
Jones told the club's official website: "I am delighted to have signed a contract extension as the ambition of the chairman and board of directors has shown me where they want to take this club.
"I am excited at the prospect of being part of that journey to take this club into the higher levels of the Football League where we rightly belong.
"The transformation at the club in the past few months has been exceptional which is why I wanted to commit my future to Bury FC."