The 34-year-old, who made a total of 279 appearances for the Blades, made the announcement at a supporters' evening in Malta.
"As I tried to step-up my rehabilitation and get as close to match fitness as possible I had to continuously take anti-inflammatory tablets to keep the swelling around my knee down," said Morgan. "I think I knew in my heart of hearts that it was time to call it a day."
The centre-half damaged cruciate and lateral knee ligaments in a Championship clash with Coventry in October 2010.
He spent last season as acting coach under manager Danny Wilson, where he guided the Blades' reserve team to the Central League and Central Division title.
Morgan added: "Danny and Frank [Barlow] were brilliant with me last season and the decision has been a lot less difficult by knowing I will continue to work in the game in a coaching capacity."