The experienced coach was at Old Trafford for more than two decades and lasted through many managers.
However, head coach Erik ten Hag has brought in Jelle ten Rouwelaar, who was previously at Burnley.
In a club statement, United said: "Manchester United can confirm that Richard Hartis has left the club after five years as senior first-team goalkeeping coach. We would like to sincerely thank Richard for his significant contribution over two spells with the club, working with a succession of first-team goalkeepers and developing numerous Academy goalkeepers, several of whom reached the top level.
“Richard was integral in our Emirates FA Cup and Carabao Cup successes in the past two years, and, in his prior spell from 2001 to 2010, he was head goalkeeping coach in our Academy and first-team goalkeeping coach in the 2007/08 season, when we won the Premier League and UEFA Champions League.
“Richard leaves with our warmest best wishes for the next phase of his career."