The 28-year-old joins the Blades as manager Nigel Adkins look to bounce back from a chastening opening day defeat at Gillingham.
Edgar spent six months at Huddersfield duiring 2014-15 and made 12 appearances.
United manager Adkins said: “David is the captain of Canada and has got plenty of experience at a higher level, including winning promotion to the Premier League with Burnley.
“He is 6ft 2in, a big presence and his versatility will be useful as he can play at centre-half or in central midfield.”
Edgar can play either at the back or in central midfield. He has been capped more than 30 times by Canada.