Krueger takes over from Nicola Cortese, who resigned in January following a reported fall-out with club owner Katharina Liebherr.
|8/13||Southampton are 8/13 to beat Norwich City at St Mary's|
Business lawyer Hans Hofstetter and Gareth Rogers, the club's current interim chief executive, have also been appointed to Southampton's board of directors.
The 54-year-old Krueger joins Southampton after working as a consultant for the Canadian men's ice hockey team during their gold-medal winning campaign at the Winter Olympics in Sochi last month.
A former ice hockey player in Canada and Germany, Krueger coached the NHL's Edmonton Oilers for just under a year before being relieved of his duties in June 2013.
The German has never been involved in football, but is determined to help Southampton maximise their commercial opportunities.
"I am honoured to take on the role of chairman of Southampton Football Club and the group," Krueger said in a statement on the club's official website.
"I have had the opportunity to meet with a large percentage of the staff at Southampton and it is clear there is a positive soul throughout the club, both at St Mary's and the training ground.
"We will build on that soul by creating platforms of open communication both inside with the staff and outside with our fan base.
"Although there is a solid foundation in place, the club still has tremendous untapped commercial potential.
"We will continue to nurture 'The Southampton Way' by reaching for consistent growth in all departments to ultimately build a culture that allows Southampton to remain healthy and sustainable in the future."