The 26-year-old England international had been strongly linked with a move to the Premier League after making a name for himself at Parkhead and sealed a switch to St Mary's on Saturday following a medical.
Forster has penned a four-year deal and will now challenge Artur Boruc, himself a former Celtic goalkeeper, Paulo Gazzaniga and Kelvin Davis for regular first-team football under Ronald Koeman.
"I really want to thank the club and the Celtic fans for all they have given me over the past four years. It has been a wonderful honour to play for one of the world's great football clubs and I wish everyone at Celtic and the supporters every success for the future," Forster told the Scottish champions' official website.
"I know the club wanted me to stay, and I know the club has done everything they possibly can to keep me, but I felt now was the right time for a new challenge in the English Premier League."
Forster came through the ranks at Newcastle United but gained experience during loan spells at Stockport County, Bristol Rovers, Norwich City and Celtic before joining the latter on a permanent basis in June 2012.
He won the Scottish Premiership three years in a row and the Scottish Cup twice, while also shining in the UEFA Champions League, with his performances paving the way for an international debut in November 2013.
Southampton boss Koeman, who has overseen a number of high-profile departures ahead of the new campaign, told his club's official website: "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 [goalkeeping coach] 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."