The 31-year-old defender is manager Steven Pressley's second signing of the summer, after the club were given special dispensation by the Football League to sign the player.
Webster, who was a free agent after leaving Hearts at the end of last season, has also played for Rangers, Dundee United and Wigan Athletic.
Pressley told Coventry's official website: "We're delighted to bring a player of Andy's quality to the football club.
"I played for a number of seasons alongside him so I'm very much aware of his footballing qualities and his character.
"I believe Andy will bring strength, leadership and aggression to our squad and will also be a vital stabilising influence on our young group of players. He is a player with good international and European experience but has served the vast majority of his career North of the border."
Webster has won 28 caps for Scotland.