Johnson, 32, has scored 92 goals for Leek in 235 appearances over four spells, having made his debut back in November 2004.
Trafford manager Tom Baker said: “Jordan is an experienced forward who has scored goals everywhere he’s been.
"He showed a real hunger to come to the club and I’m excited to work with him. He can play anywhere across the front line which is great."
A British Virgin Islands international, with two goals in six caps, Johnson has played for Congleton, Newcastle Town, Telford United, Chasetown, Northwich Victoria, Airbus and Kidsgrove Athletic.
Chairman Jon Eeles said: "Jordan spoke to me last night to informed me of the decision, and that he was gutted to leave Leek Town.
“The Club holds many special memories for him and he hoped to finish his career here.
“However, now he lives in St Helens, playing in the South-East league of the NPL was not something he could commit to. We wish Jordan all the best and hope he wont be a stranger to the Club in the future."
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