Goal revealed the Gunners' interest in the 19-year-old earlier this month and, after agreeing personal terms over the weekend, the England Under-19 international becomes the fifth player to leave St. Mary's this summer as the south-coast outfit's firesale continues.
The teenager, who will cost an initial £10m, becomes the latest Southampton academy product to move to the Emirates Stadium, following in the footsteps of Theo Walcott and Alex Oxlade-Chamberlain.
Liverpool boss Brendan Rodgers had also been keen on bringing Chambers to Anfield, but the youngster opted instead to sign for the north Londoners and is excited about the prospect of working under Arsene Wenger.
"I am so happy to be signing for Arsenal. 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," he told the club's official website.
"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."
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Wenger has hailed Chambers's versatility, being able to play across the back-line and in midfield, and is excited at the player growing into his potential at the Emirates Stadium
Wenger added: "We are very pleased that Calum has agreed to join us. The way he adapted to the Premier League last season with Southampton at a young age shows that he has tremendous quality.
"He has a lot of the attributes that we look for in a young player and I am sure that he will do well with us."
Chambers could be joined at the Emirates by former Saints team-mate Morgan Schneiderlin, with Arsenal redoubling their efforts to sign the French midfielder to beat off competition from Tottenham.