Heathcote signs from NPL West Division side Runcorn Linnets, who confirmed his departure over the weekend.
He was top appearance maker for the Yellows last season, making 54 appearances in all competitions. He scored six goals during that time, including one against Macclesfield in the Cheshire Senior Cup.
Meanwhile, Peers joins the club from National League North side Curzon Ashton. He made 11 appearances, scoring five goals during that time.
Campbell also joins from Curzon Ashton. The 20-year-old came through ranks at Port Vale and Salford City, before signing for Stalybridge Celtic, Altrincham, FC United of Manchester and Marine.
Finally, Johnstone, the brother of Crystal Palace goalkeeper Sam, has joined as the new number one. He has previously played for Fleetwood Town, Manchester United, Sunderland, St Johnstone and AFC Fylde.
All will be hoping to help Macclesfield adjust to life at step three.