The 22-year-old player is the Saints' first signing since the end of last season and the departure of Dutch manager Ronald Koeman to rivals Everton last week.
No financial details were given but British media put an 11 million pound price tag on the deal.
"Nathan has gained plenty of experience in the Premier League with Norwich City, showing his quality at the top level on a consistent basis," said Southampton's executive director of football Les Reed on the club website (www.saintsfc.co.uk).
"He has also performed exceptionally well on the international stage, playing a key role in helping England Under-21s win the Toulon Tournament this summer.
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"He has the potential to continue developing and becoming an integral part of the squad for years to come," added Reed.
Redmond joined Norwich from Birmingham City in 2013, making 122 appearances for the Canaries and scoring 13 goals.
Southampton finished sixth last season and secured a place in the Europa League.
(Reporting by Alan Baldwin. Editing by Adrian Warner.)
