The 19-year-old right-back, who can also play in midfield, made 21 league appearances for the Saints last season having progressed through the club's youth academy.
He becomes Arsenal’s fourth signing of the summer following the arrivals of Alexis Sanchez, Mathieu Debuchy and David Ospina and has penned a "long-term" contract with the Gunners.
"I am so happy to be signing for Arsenal," Chambers told the club’s official website. "They are a team I have much admired for their playing style, and a team who have been one of the top sides in Europe for many years.
"I'm looking forward to joining up with my new team-mates today and beginning preparation for the season ahead.
"I would like to take this opportunity to say thank you to everyone at Southampton FC for everything they have done for me and for making this move possible.”
Southampton have already sold Rickie Lambert, Adam Lallana, Dejan Lovren and Luke Shaw to rival Premier League clubs this summer, with Morgan Schneiderlin also the subject of speculation linking him with Arsenal and Tottenham.