The 64-year-old had three stints with the Swans during his playing career and has since worked for them in various capacities, including caretaker manager.
"I know how respected and important he is at this football club," BBC Sport quotes Potter as saying.
"Nobody knows the football club better than him. He brings an experience and quality that will prove really valuable to us.
"He will support the environment here. He is someone for all of us to draw on his experience, mentorship and support. Alan is an important person to have around and I'm excited to be working with him."
Curtis served as the Swans' interim boss following Bob Bradley's sacking in December 2016.