After two years at Parkhead, Hammond will “pursue new opportunities” a short statement on the club website confirmed.
Hammond previously held similar positions as director of football at Reading and was West Bromwich Albion technical director before his spell in Scotland.
His departure follows the resignation of Neil Lennon last month plus the impending exit of club captain Scott Brown and chief executive Peter Lawwell in what is now becoming a significant summer of change in the east end of Glasgow.
The club is still seeking a new permanent head coach to replace Lennon, who stepped down from his role in February. Major shareholder Dermot Desmond said the process in identifying his replacement is underway earlier his month.
Chief Executive Lawwell said: “We would like to thank Nick for his contribution to Celtic across the past two seasons. Everyone at the club wishes Nick the very best for the future."