The 24-year-old, who spent a season on loan with Stanley in 2009/10, has penned an initial 12-month contract.
Coleman told the club’s official website: “Billy’s a proven goalscorer at this level.
“He didn’t have the best of times last season and I think he’s keen to put that right. He’s a player who suits our style of football and we think he’ll do well for us.
“We’ve always known that he’s a good player. He was only a young kid when he came to us the first time but he already had an eye for goal and he’s one of those lads who you always know what you will be getting when you sign him.
“He’ll always give it his best shot, he’s a smashing character around the place, he loves football and sums up what we’re trying to achieve here.”