The Northern Ireland international has joined for an undisclosed fee from Norwich City and has signed a three year deal.
He made 43 appearances for relegated Norwich last season and has also played for Chesterfield and Nottingham Forest.
Clingan takes penalties and free kicks and has been brought into replace Danny Fox.
Norwich boss Bryn Gunn said to his club's official website: "We thank Sammy for his services to the Football Club. He came in last season on a Bosman transfer and the fee we have agreed with Coventry is the right for Sammy's place in the market.
"He has gone back to the Championship and I'm sure will help Coventry City in that division and feel he could take the next step up to the Premiership if needed.
"In many ways we are sad to see him go but we realise his ambition as an international player and wish him well with his future career."