The highly-rated 17-year-old has signed a three-year contract at St Mary's, although he will not be eligible to play for the first team yet as he has joined outside the transfer window.
Stephens has made three starts and three appearances from the bench so far this term and was reportedly also interesting Newcastle, Sunderland, Bolton and Fulham.
Saints manager Nigel Adkins told the club's official website: "At the end of the day what we are trying to do is make sure we have good, young talent at this football club.
"Plymouth are in a scenario at the moment where I'm sure they don't want to lose players, but we are out there actively working very hard to improve the group of players we have coming through the system.
"He has been on the radar for a while."
Source: PA
Source: PA