Ball who scored 11 times for County during this season joins Dino Maamria's side with his new boss having been in charge of Nuneaton Town earlier this year, writes Tom Feaheny.
An undisclosed five-figure fee has been paid for the former Stalybridge Celtic midfielder.
“I am absolutely delighted, I look forward to getting started and trying to help the team achieve our goals," Ball said to Stevenage's website.
"It was a good season for Stockport getting into the play-offs that was always the ambition at the start of it all.
"I played against Dino's team twice and he must have been impressed with what he saw."
Ball says that after impressing at County, he wants to do the exact same thing at his new club.
“I want to be a big player for the club and I can’t wait to show the supporters what I am all about.”