The 21-year-old becomes new manager Mauricio Pellegrino's first addition and will link up with the Saints later this month due to his involvement at Euro 2017.
Centre-back Bednarek, who reportedly cost £5million, told the club's official website: "I am so happy that I could join a club like Southampton.
"This is the moment I have worked for that makes my dreams come true.
"It only gives me motivation to work hard, to show my skills and to help Southampton to get better and better.
"I think it's a good step for me, because I have heard Southampton is such a good club for young players, so I can improve here."
Fellow defender Jack Stephens has also signed a new five-year deal at St Mary's.
The 23-year-old impressed after nailing down a first-team place following Virgil van Dijk's season-ending injury in January.
England Under-21 international Stephens, who has been with Southampton since he was 17, is highly rated by the club.
Executive director Les Reed said: "Our philosophy at Southampton is to turn potential into excellence, and Jack is somebody who very much embodies this.
"His progression, and the level of his performances, was one of the real highlights of last season, and we have been delighted with his development ever since he joined the club."
Stephens said: "I am absolutely delighted to extend my stay."It feels like home to me. I have really enjoyed my time here and am now looking forward to the next five years.
"It's a massive platform for me now because it just shows how much faith the club have put in me."
Southampton also announced striker Sam Gallagher has put pen to paper on a new four-year contract.
The 21-year-old spent last season on loan at Blackburn, but made an impression with 12 goals despite their relegation from the Championship.
Gallagher said: "This contract shows the belief that the club have in me and I need to prove that now, which is what I am hoping to do in pre-season.
"I definitely thank Blackburn a lot for last season. It has helped me grow both as a person and a player. It's a club that I have massive respect for."
