The youngster has signed a long-term deal with the Emirates club.
The fee was undisclosed but believed to be worth £16m, this despite the fact that the 19-year-old full-back has only made 18 Premier League starts.
The England U19 captain has made his name as a full-back but can also play in midfield or as a centre-back.
"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," said Arsenal manager Arsene Wenger.
"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 added: "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. I'm looking forward to joining up with my new team-mates today and beginning preparation for the season ahead."
Southampton Head of Football Development Les Reed admitted he was disappointed to use yet another young star: "We are naturally disappointed whenever any of our Academy graduates leave and that is very much the case with Calum’s departure,” he said.
"Our position remains unchanged in that we are determined to keep our best young players at the club.
“It is important in the transfer window to remain calm, resilient and above all patient.
“We have targets, and we are working hard to get them across the line.”
Southampton have already seen a host of talent leave the club this summer. Adam Lallana, Dejan Lovren and Rickie Lambert all left for Liverpool for a combined sum approaching £50m while teenage left-back Luke Shaw joining Manchester United for a fee believed to be £27m which can then rise to £30m.
Head coach Mauricio Pochettino also left for Tottenham and there have been doubts over the future of French midfielder Morgan Schneiderlin.
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