The club's former defender resigned from his position in charge of Clyde to take over the post, which was vacated by Kenny Shiels in the wake of the club's 10-2 defeat at Hamilton, which followed their relegation from the Championship.
Morton made the announcement on their official Twitter account saying: "The club would like to welcome back Jim Duffy to Morton - our new first-team manager.
"Jim played for Morton in the 80s, playing over a hundred matches over three years at the club."
Duffy, who has managed Falkirk, Dundee (twice) and Hibernian with a spell as caretaker at Norwich City before a season at Brechin City preceded his move to Clyde in 2011, said: "Morton are a club I know well and I am excited by the challenge. I have really enjoyed my time at Clyde however I could not turn down the chance to be involved at Greenock."
The former Morton manager Ian McCall and the Dundee coach Matt Lockwood had also expressed their interest in the job.