Thompson, 27, previously played under Dolly Blues boss Mark Fell, and has attracted interest from several NPL clubs.
Fell said: "He’d head bricks if you asked him to, he’s got great physical and technical attributes for a defender and just as important a massive desire and will to win.
"He’ll benefit from the professionalism in our dressing room and I think he’s got the potential to step up to be a top defender."
Thompson will join up with the rest of the Lancaster squad for the start of pre-season training on June 29.
He said: "I’m really looking forward to a new challenge, it’s a step up in standard that I’m ready for and the way the club has progressed since the gaffer went there shows we can be towards to sharp end of the division.
"It’s a great club and I was keen to get working with Felly and Lanky again and I’ve seen first hand the excellent support the club has from a great set of fans."