The Sunderland-born 22-year-old scored 15 goals last season for the Blue Square Bet Premier side and, having spent his entire career in non-league football, believes now is the time to make the step up.
It was announced on Wednesday that transfer target Gillies would link up with Carlisle for pre-season training despite the League One club still trying to finalise an agreement with Gateshead, but the deal has now been completed.
"I just want to get on with this now," he told the club's official website.
"It's been a frustrating five weeks but I only ever really wanted to come here. I've met the lads and the next thing for me is to do as well as I can in training so that I can hopefully earn a place in the team."
Manager Greg Abbott was equally optimistic about Gillies' ability to move up the divisions, adding: "Josh now has a fantastic opportunity to take the step into professional football. We think he's ready to do that.
"There is work for him to do, but his attitude and desire to succeed are there. We're all really looking forward to working with him."