"The club would like to place on record its thanks to goalkeeping coach Gary Walsh, who has opted to leave the KCOM Stadium to take up a role with Aston Villa," read a statement on Hull's official website.
"Having joined the Tigers during the 2011/12 season, Walsh was part of the coaching staff during the most successful period in the club's history, assisting in two promotions to the Premier League as well as the 2014 run to our first-ever FA Cup final appearance.
"The former Manchester United goalkeeper was in the Tigers' dug-out for the final time during Saturday's Premier League fixture at Watford and leaves with our very best wishes for the future.
"The process to recruit a replacement is now underway."
Walsh's departure means current manager Mike Phelan is the only member of the coaching team which guided Hull to promotion in May still at the club.
Bruce resigned as Hull boss in July after becoming increasingly frustrated by the lack of investment in the playing squad and former first-team coach Keith Bertschin left the KCOM Stadium by mutual consent in August.
Phelan, who installed Neil McDonald as his new assistant last week in place of Clemence, was already looking to add at least one new member to his backroom team and will now begin his search for a new goalkeeping coach.
Walsh arrived at Hull under former boss Nick Barmby in December 2011 and Phelan had been hoping the ex-Manchester United and Middlesbrough goalkeeper would stay in East Yorkshire.