The 26-year-old has joined the club on a four-year deal for a fee believed to be in the region of £10million.
Sky Sports reported on Friday that Forster was travelling to the south coast to discuss personal terms after the clubs agreed the transfer, and he underwent a medical on Saturday.
In moving to St Mary’s, Forster is reunited with England goalkeeper coach Dave Watson.
Saints boss Ronald Koeman said: “Fraser is a very talented player and we are delighted to be able to bring him to Southampton.
“This is another important part of our rebuilding process ahead of the start of the season.
“The fact that he has worked with Dave Watson before means we already know all about his strengths and weaknesses, and I am confident that we will be able to help him improve even further.
“Fraser is the perfect fit to help complement the players we already have, and he will add a lot of quality to the squad.
“He is an exciting English player with a very good reputation within the game and, at 26, he will enjoy the best years of his career at Southampton.”
Forster becomes the second former Celtic goalkeeper in the Southampton squad; Artur Boruc, who was the club's No 1 last season, spent five seasons with Celtic before joining Fiorentina in 2010.