Rutherford, 23, will offer Moors` boss Jason Ainsley more attacking options and provide competition for Glen Taylor and Bradley Fewster.
Rutherford began his career at Hartlepool United, going on to make nine appearances, before moving south to join Dover Athletic.
Spells in Scotland with Alloa Athletic, Arbroath and Berwick Rangers followed, before Blyth secured his signature in October 2017.
Rutherford joins Moors having previously won Scottish League Two player of the month in March 2017 whilst playing at Berwick Rangers.
Ainsley was delighted after a deal was struck for the striker. He told his club`s official website: “Greg scored 8 goals for Blyth, despite not starting a lot of games for them.
“Tommy Miller and I have been conscious if anything happens to Glen we do not have a like for like replacement for him and in Greg, who is 6’2”, we feel he is the answer to that problem.
“We are going into a very busy couple of months in which we will be playing Saturday/Tuesday, so we feel Greg is a welcome addition to our squad.
“At 23, Greg has a lot of experience both in Scottish and English football and we hope he has a successful time with us”.