Scotland cap Webster enjoyed spells at Hearts, Rangers and Dundee United but was released by Coventry City.
The 33-year-old will be included in Saints' squad for tomorrow's Championship clash with Livingston, subject to international clearance.
Webster said: "Hopefully I can bring a bit of experience, not just to the defence but to the group as a whole."
Manager Ian Murray has been keen to acquire the defender's services for some time to help young defenders Sean Kelly and Jack Baird.
But there was interest from other clubs in Webster, who spent two seasons with Coventry after leaving Hearts and made 34 appearances last season for the English League One club.
"It has been ongoing for a bit," Webster told St Mirren's website. "Initially I was in to train and then the manager asked me to come into the football club and I was delighted to make that decision.
"The manager's eagerness to get me in, allowing me to come in and train and that feeling of someone wanting you.
"I took my boys to the Dumbarton game here and the staff were like 'come in, have a cup of tea', all these kind of feel-good factors around the football club, these are all important things."
Webster is the Buddies' second signing in as many days, after Murray added 20-year-old Aberdeen striker Lawrence Shankland to his squad on loan on Thursday.
Murray said: "The way Andy goes about his training and the way he plays the game will be huge for us.
"To finally get him is good news for us.
"Andy is an out-and-out centre half, he'll certainly organise players and he's a fantastic player for Sean and Jack to learn off, he'll help them enormously.
"Andy goes straight into the 18 along with Lawrence."
Shankland, who joined Aberdeen from Queen's Park in 2013, scored seven goals in 13 appearances for Dunfermline Athletic while on loan to the League One club last season.
St Mirren have signed veteran defender Andy Webster on a one-year deal, with the option of a year's extension.