The switch marks a busy few days for the Sky Blues after they secured the signature of Derby County forward Martyn Waghorn.
Moore joins Coventry on a three-year deal after his five-year spell at United came to an end at the end of last season.
City manager Mark Robins said of the transfer: “We’re very pleased to welcome Simon to Coventry City.
“Simon is a very good goalkeeper and is a great professional with a top attitude, who will strengthen our options in this area.
“He brings great experience too, with time in the Premier League and the Championship under his belt.
“We look forward to working with him.”
Moore made 70 appearances for the Blades, turning in some stand-out performances particularly in the promotion from League One to the Championship in Chris Wilder’s first season in charge.