West Brom have sacked Nicolas Anelka citing "gross misconduct" after the striker claimed on Twitter he had quit the club.
Mauricio Pochettino expects to be at Southampton next season and is looking forward to working with chairman Ralph Krueger.
The former Scotland international has agreed to extend his contract until the summer of 2014.
The deal also includes an option to increase it by a further 12 months.
Thompson, 34, has enjoyed the best goalscoring form of his career with the club he supported as a boy.
The former Dundee United and Rangers player returned to Scotland in 2011 after spells with Cardiff and Burnley and has since struck 30 goals in 72 appearances for St Mirren.
He told St Mirren's official website: "I am very happy here at St Mirren, it was the easiest football decision I have ever had to make and I look forward to being involved in the continued progress of the club."
St Mirren manager Danny Lennon added: "These two seasons have been the best form of his career. He has been our top scorer for two years, led the line incredibly well and is a character that motivates the players around him.
"He has played a huge role in our success and raising the profile of our club.
"I am delighted Steven has decided to finish his playing career at the club that inspired him to play this beautiful game."