The Italian, who is 29 on Tuesday, has agreed a three-year contract to link up again with manager Ronald Koeman.
Pelle scored 55 goals in 66 matches for Feyenoord under Dutchman Koeman, who was named Saints boss on 16 June.
We need more players to bring the squad to where we need and expect
The former Parma player said: "This is going to be the best choice for me because the club wants to keep improving every year."
He is Saints' second signing of the summer, following the £10.9m arrival of FC Twente attacking midfielder Dusan Tadic.
Pelle initially joined Feyenoord on loan from Serie A side Parma in 2012, before joining the Dutch club on a permanent basis in January 2013.
He moves to St Mary's after Saints sold England striker Rickie Lambert to Liverpool for about £4m last month.
Koeman said: "We needed a good player in that position.
"He's a tall striker with a lot of movement and he's fast. He's a player who gives confidence to the team because he keeps the ball."
Koeman expects to make more signings as he rebuilds his squad following the departures of Lambert and midfielder Adam Lallana to Liverpool, and defender Luke Shaw to Manchester United.
"We know that we need some more players because we haven't occupied all of the positions," the 51-year-old said. "We need more players to bring the squad to where we need and expect."
Saints centre-back Dejan Lovren remains a target for Liverpool, who had a £20m bid for the player rejected last week.
Southampton have signed striker Graziano Pelle from Feyenoord for an undisclosed fee.