The 28-year-old was a title winner with the Silkmen last season and joins on an 18-month deal.
Blissett has previously played for Kidderminster Harriers, Torquay United and League One side Plymouth Argyle.
Moors assistant manager Gary Whilds said the striker's attitude makes him an easy fit.
“Nathan has a great record at getting promoted from this level and even in the Football League," he said.
“He will massively add to our frontline and, most importantly, Tim [Flowers] and I have worked with him before.
“He’s good on the pitch and is the right type of person to bring in – he’ll add to the group off-the-pitch as well with his attitude.”
Blissett could be in line to make his debut against Barrow tomorrow afternoon.