Scowcroft, who spent the latter parts of last season on loan at former club Ipswich Town and who was released by Craig Levein at the end of the campaign, has signed a three-year contract with Micky Adams' side.
"James is a player who is proven at the top level," said Sky Blues boss Adams.
"He has a lot of qualities and can play in a variety of positions across the front line. I worked with him at Leicester and I know that he will be a very valuable addition to our squad."
Scowcroft spent four years at The Walkers stadium following his move from Ipswich, making 147 appearances and scoring 27 goals.