Earlier this week the Sky Blues completed the signing of former Reading striker Mathieu Manset. having been placed into a rolling embargo by the Football League following their exit from administration.
City can now sign players under supervision from the Football League, on a one-in-one-out basis with Manset replacing the departed Cody McDonald and now Webster replacing David Bell.
Webster has played the majority of his top flight football at Hearts where he played alongside Pressley for five seasons.
He has also enjoyed spells at Rangers, Dundee United and Wigan Athletic as well as amassing 28 full international caps for Scotland.
Pressley said: “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.
“After speaking with him it was evident to me he was ready for a new chapter in his career and I believe that this football club can provide him with a platform in which to do that.”