The 54-year-old Canadian-born German coached the Edmonton Oilers in the NHL during the 2012/13 season, and the Swiss national team from the 1997/98 season through to the end of the 2010 Vancouver Winter Olympics.
He was a special adviser to the Canada squad in Sochi.
"Ralph has an impressive background in major league sport at all levels," Southampton owner Katharina Liebherr said in a club statement.
"It is his experience as an expert in leadership, motivation and team-building that makes him ideally suited for this important position," she added.
Outside of sport Krueger has been closely involved in the World Economic Forum think tank since 2011.
"It is clear there is a positive soul throughout the club, both at St Mary's and at the training ground," said Krueger, capped 45 times by the West German national ice hockey team.
SOLID FOUNDATION
"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."
After a barnstorming start to the season, Southampton have stalled, and now sit ninth in the 20-team table, a comfortable 11 points ahead of 10th-placed West Ham United.
Much of Southampton's renaissance has been credited to Argentine manager Mauricio Pochettino, who had enjoyed a close relationship with former chairman Cortese.
Fears of the manager leaving at the end of the season would seem to be receding, and local media report the club is working on a deal to keep Pochettino at St Mary's with a new deal.
Liebherr added: "The news that Ralph has agreed to take on the role (of chairman)... follows a calm and steady process of identifying a board that will bring stability needed to achieve long-term success both on and off the pitch.
"I will remain on the board, with an active involvement, and we will continue to move forward with great respect for Saints' history, while at the same time working towards a process that is creative, unique, dynamic and modern."
(Writing by Ossian Shine; Editing by Ken Ferris)
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