The former German ice hockey international's contract was set to end in June and following recent talks with Southampton shareholders Jisheng Gao and Katharina Liebherr, it was agreed by all parties that the deal would not be renewed.
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. 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.
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.