Former England striker Beattie will take on his first managerial assignment, having scored seven times in 27 appearances for Stanley last term, on the back of Leam Richardson's departure to become Paul Cook's number two at Chesterfield.
Coleman, Cook's predecessor at the club, masterminded Stanley's return to the Football League during a 12-and-a-half year reign and is currently out of work following an unsuccessful 12-month stint at Rochdale.
He was one of seven candidates interviewed by Store First Stadium chiefs on Monday but rookie Beattie got the nod.
"He obviously had to be considered," said Heys of Coleman. "He had a fantastic time here at the club, he got us into the Football League.
"The whole idea of getting Accrington back into the Football League, very few people would have believed it, but John made that possible, kept us in the Football League and did very well for us.
"It was a really difficult decision on Monday at the interviews. We interviewed seven people and over half of them could have done a good job at Accrington Stanley, if not all of them.
"We spend a good while talking about the pluses and minuses of all the candidates and it was James that won through."