"Ralph represented our club with honour and integrity, and followed the Southampton way with great passion. We thank him for the foundations he has helped to build and wish him well for the future," Chinese businessman Gao said in a statement.
Liebherr said Canadian-born Krueger, 59, had laid the foundations for Southampton to be a sustainable team that put pressure on the top sides in the Premier League.
"He was a true leader who fully embodied the Southampton way, a culture which will live on strongly beyond his time as chairman," Liebherr added.
Krueger's departure comes nearly four months after vice-chairman Les Reed left the club to become the English Football Association's new technical director succeeding Dan Ashworth.
"Everything has a beginning and everything has an end. It's the journey in-between that I'll treasure. Thank you Southampton Football Club for the journey," Krueger said.
Former NHL coach Krueger's tenure at the south coast club has not entirely been smooth, as he oversaw the appointment of five different full-time managers with current boss Ralph Hasenhuttl being the latest in December.
Southampton also narrowly missed out on silverware in 2017 when they were beaten 3-2 by Manchester United in the League Cup final. They then just managed to avoid relegation last season.
Saints, who are 17th in the table with 33 points from 32 games, said they would provide more information about their future leadership structure at the end of the season.
(Reporting by Shrivathsa Sridhar in Bengaluru; Editing by Christian Radnedge)
