Armstrong has signed a four-year deal at St Mary's, with the fee for the 26-year-old reported to be £7 million ($9m).
The Scotland international, who has been named in the PFA Scottish Premiership Team of the Year three times, won four league titles during his time at Celtic.
"Stuart is a player who we have admired for some time, and I am delighted we have been able to bring him here, especially given the competition we faced to sign him," said Southampton manager Mark Hughes.
"We have strong players in the squad and it is important we build on that by adding different qualities. It is important we add a greater goal threat to the team as a whole, and to our midfield specifically, and Stuart's record of scoring and creating makes him an extremely exciting addition in that area.
"He brings with him extensive experience of European football and has developed his game impressively over the past few seasons at a major club in Celtic, where there is a demand not only to perform but also to win. Stuart has done both during his time there.
Armstrong has won six Scotland caps since making his debut for the national team last year.
"Southampton seems a really good fit for me. Watching from afar, I really enjoy the attractive football that they play and I'm very happy to be here," added Armstrong.
"Every season, I put demands on myself to create and score goals. I hope going forwards from here that it will be the same this term at St Mary's."