The 26-year-old had been a free agent after being released by the Blades at the end of last season.
Following a successful trial, Miller has now become part of the Sky Blues squad for the new campaign.
"I'm delighted to bring in Shaun Miller. He is a player whose situation we have monitored over the course of the summer," Coventry boss Steven Pressley told the club's official website.
"He has now trained with us for a 10-day period, in which he impressed us greatly. First and foremost, he is a player that possesses terrific work ethic. He also brings terrific movement and finishing ability.
"He is at a great age of 26 and I believe he can become a prolific goalscorer for this football club."
Miller is the League One club's seventh signing ahead of the new season.