The 23-year-old has been a consistent performer for the Somerset side since signing from Yate Town in 2015.
Formerly with the Bristol Rovers and City academies, he had a particularly successful 2016/17 season when he scored 22 goals in forty-one games and has 11 from twenty-six to date this term.
Chippenham manager Mark Collier told his club`s official Pitchero website: "I tried to sign Jake in the summer and I have continued to monitor his progress since then. His goal record in the past season and half has been outstanding, and I have no doubts he can make the transition from Southern League to the National League South.
"I am particularly pleased to get the deal over the line as other clubs in the National League were chasing his signature.”
Jackson will be ready for the New Year`s Day clash at home to Hungerford Town.