The 33-year-old had spent two seasons with the Red Imps, but was allowed to move on as manager Peter Jackson decided to reshape his squad.
Magpies boss Ian McParland told the club's official website: "I am delighted that Jamie has agreed to join us.
"He had the opportunity to stay at Lincoln, but has chosen to come here and I am looking forward to seeing his name appear regularly on the scoresheet next season.
"His track record speaks for itself. Although he is 33, he is still a fit lad who chalks up the appearances every year and he is also a chirpy character who will be good for our dressing room."