It is the 42-year-old's first senior role in management.
Shelbourne are back in the top flight of the Ireland football division after spending last season in the second tier.
Duff has previously spent time on the coaching staff of Celtic and the Ireland national team.
"I'm delighted to take up the manager's position at Shelbourne," he said.
"Having coached and managed our U17 National league team and been around the club, I can see the plans and ambition in place here and am excited to begin a new chapter of Shelbourne’s 126-year history.
"I’m extremely passionate about youth development in Ireland and about Irish football in general and see this as a great opportunity to help build something that both the club, its fans and myself can be proud of.
"With the club now in the SSE Airtricity League Premier Division, and the foundations being put in place by the board and its directors, I can’t wait to start."
Duff spent three seasons at Chelsea as a player and was part of the sides that won two Premier League titles under Jose Mourinho in the 2004/2005 and 2005/2006 seasons.
Duff also played for the likes of Blackburn Rovers, Newcastle United and Fulham, and won 100 caps for the Republic of Ireland national team, scoring eight goals.
