Former Gainsborough Trinity chairman Swann was named as successor to Steve Wharton at a board meeting at Glanford Park.
Wharton stepped down at the end of the season after spending 11 years during two different spells in the role.
Swann, chairman at Gainsborough for five years, recently joined the board of directors at Scunthorpe with a view to succeeding Wharton.
A brief club statement read: "Peter Swann has been appointed as the new chairman of Scunthorpe United.
"He was voted onto the board of directors by the current board before then being voted in as chairman.
"He replaces Steve Wharton, who resigned as chairman following the final game of last season against Swindon Town."
Scunthorpe were relegated from the Championship in 2011 and after two seasons in League One dropped into the bottom tier this season for the first time since 2005.