The 40-year-old Scot was first team coach under manager Gary McAllister at The Sky Blues and took up the managers role at Highfield Road when McAllister quit for personal reasons last December.
He took The Sky Blues to the brink of the Division One play-offs last season only to lose his job when they announced Peter Reid as their new boss with just one game remaining.
Black has been appointed following Mark Bowen's shock departure from Blues last month and will begin his new first team coaching duties when the squad report back for first team training this Thursday.