The 24-year-old Irish striker spent last season on loan at the Crown Ground from Pacos de Ferreira and has agreed a one-year deal following his release by the Portuguese outfit.
Amond scored nine times during the campaign and was named voted Player of the Year by Stanley's supporters.
"I'm delighted to be back," he told Accrington's official website.
"I had to go back to Portugal and sort one or two things out. It was a bit weird going back over there for pre-season, the manager quite liked me but the president didn't want me."