A statement from Saints chairman Rupert Lowe said the former Leeds captain left by mutual consent after a meeting with Lowe yesterday.
Reserve team boss Steve Wigley has taken over as first team coach until the end of the season.
Strachan, 47, praised the club, which appointed him when they were in the Premiership relegation zone in October 2001.
He said: "This is a truly great club with a truly great squad of professionals and it is with regret that I am leaving for my own reasons. The chairman and I feel this to be the best course of action.
"Steve Wigley will do a first class job between now and the end of the season and I fully support his interim appointment."
Lowe issued a statement that read: "I can assure all our supporters that we are taking the appointment of Gordon's successor very seriously and will take the necessary time to explore our numerous options.
"An appointment will be made when we are ready, but in the meantime, it is the football which must come first."
He added: "Gordon has done a great job for us during his two-and-a-half years tenure and, unusually in football, leaves us on the very best of terms.
"He and his family will always be welcome at our club while I remain chairman."
In his time as Saints boss Strachan breathed new life into the South coast club.