There’s been somewhat of an overhaul at Chester since the arrival of joint managers Bernard Morley and Anthony Johnson and Archer becomes the latest player to leave.
The 24-year-old played 19 times in the league last season, scoring four goals but signs a two-year deal at Gigg Lane.
He becomes the second Chester player to move into League football this season following the departure of Tom Crawford to Notts County.
Speaking to his new club’s website, Archer said he was eager to get started.
“It's a step up in my career; I can't wait to get going and repay the club for bringing me to the Football League.
“I’m confident I can make the step up to the League. I'll hopefully repay the club's faith by scoring goals and working hard for the team and Manager.”
Chester begin their National League North campaign against Spennymoor Town on August 4.