Robins, 47, has returned to the Sky Blues for his second spell as manager, having been in charge between 2012 and 2013 before leaving for Huddersfield.
He has rejoined Coventry, who are bottom of League One, on a contract "beyond the current season".
Slade was sacked on Sunday with the club 13 points adrift of safety.
More to follow.
Coventry City have appointed Mark Robins as the League One club's new manager, a day after relieving previous boss Russell Slade of his duties.