Rovers thanked Morton and said there was “an extensive recruitment process over the past couple of weeks”, with Imrie showing “real passion and a clear understanding of our squad and ambitions”.
Andy Millen will follow Imrie from Greenock to Kirkcaldy as assistant, with their first challenge being in the Scottish Cup third round against Alloa Athletic on Saturday.
Chairman Colin Smart said Imrie “was the standout candidate” because of “his ambition and energy”.
He thanked centre-half Paul Hanlon and coach John Potter “for their professionalism and leadership over the past two weeks in guiding the team through an important spell”.
Morton, who say an agreement was reached with Rovers said in a website statement: “We have consistently maintained that we would not stand in Dougie’s way.
“Although the club is disappointed, we respect Dougie’s decision. He stepped into his first managerial role at a very challenging time, with the club sitting at the bottom of the Championship, and played a pivotal role in stabilising our position.
“His tenure brought solid league finishes, near misses in the promotion play-offs and memorable cup performances.”
Former Motherwell, Derby County, Preston North End and Nottingham Forest manager Billy Davies, who was appointed technical head coach this summer, will take interim charge as Morton “begin internal discussions regarding the next steps”.
