Gilchrist, 24, scored 26 times to top the goalscoring charts, before spending the back end of last season at Stockport, where he picked up a title winners medal.
South Shields joint manager Lee Picton said: “We are delighted to bring Jason to the club.
“He is someone we have tracked for a while and he has a proven goalscoring record at this level and higher.
“We feel he is a great fit for what we are looking for moving forwards at the club.
“We’re really confident he will suit our style of play, and have been very impressed with him as a person during the conversations we have had with him.”
Gilchrist came through the Manchester City youth system, spending 10 years at the club, before moving on to Burnley’s development teams.
He played senior football for Droylsden, Accrington Stanley and Chester before moving to FC United in 2016, scoring 29 goals in 15 months to earn a move to Southport.