The young keeper is the first of two signings in that position Trinity boss Dave Frecklington is hoping to make.
The Trinity manager told the club`s official website: "I am still searching for another goalkeeper, who will push Richard all the way and fight for the number one spot.
“No-one is guaranteed a shirt, but if the players are putting in the performances, they will keep the shirt. The players that impress me the most during pre-season will be the ones that put themselves in pole position for a starting jersey come August 5th, but until then, everyone has the chance to stake a claim for the shirt."
On agreeing his deal to join Gainsborough, Walton revealed: "It’s good to be here, it has been in the pipeline for a while. When I sat down and spoke to Lincoln manager Danny Cowley at the end of the season, he told me of the interest from Gainsborough and it was something I really wanted to do. I wanted to get my Lincoln deal sorted first though. Having worked with Dave Frecklington a couple of times, I know him well. As a 17/18-year-old, I spent time at Lincoln United with him and then I had another month with him last month at Spalding United."
Walton will continue to train with Lincoln during the week where he will work with Imps` first-choice keeper Paul Farman and their experienced goalkeeper coach Jimmy Walker.