In addition to finance, Bang will be responsible for the company's legal and property council in his new role.
He succeeds Anders Hagh, who stepped in as the retail group's chief executive officer in April of this year.
Commenting on his appointment, Hagh stated, "Peter is a skilled leader and distinct team player with his values compass in order. For that reason, I am particularly pleased that we have succeeded in getting Peter on board."
Peter Bang previously served as the finance chief of multinational window manufacturing firm, Velux, for the past 19 years.
He is a board member and chairman of the audit committee in Solar Group, an international sourcing and service company within electricity, plumbing, climate and energy solutions, with a strong focus on digitisation and ESG.
He is also the chair of the board of the international Swedish company BIMobject, which works with digitisation and sustainability within the construction industry.
"In addition to an enormous professional background and great results at the large international company Velux, [Bang] comes to Salling Group with a dedicated customer focus and great commitment to the people around him," Hagh said of the new appointment.
"This has been crucial for us in our search for a new CFO. Peter will further enhance our already strong work in the area of finance and ESG, and he is in every way the best suited for the role."