The 27-year-old left-back, who has been ousted from the first team by youngster Luke Shaw, joins the Championships side on an initial loan before activating a permanent deal
The 27-year-old had been at St Mary's Stadium since 2011 and will move to the Championship side until the end of the season before concluding a permanent switch at the end of the campaign on a three-year deal.
|17/2||Southampton are 17/2 with Bet365 to beat Fulham 2-1|
"Danny was an extremely popular member of the dressing room and leaves with the club's best wishes for his future career," read a statement on Southampton's official website.
"He will be fondly remembered for the role he played in helping Southampton return to the Premier League and will always be warmly welcomed back to St Mary's."
Fox's arrival comes a day after Algerian forward Rafik Djebbour moved to the City Ground from Olympiacos on a two-and-a-half-year deal.
Meanwhile, defender Aaron Martin has signed for Birmingham City a day after being released by Southampton.