The transfer fee for what Arsenal called a ''long-term'' deal was undisclosed but is thought to be in the region of >16 million ($27 million).
Chambers continues the exodus of players from Southampton this summer, following the departures of Adam Lallana, Rickie Lambert and Dejan Lovren to Liverpool and Luke Shaw to Manchester United.
''We are very pleased that Calum has agreed to join us,'' Arsenal manager Arsene Wenger said. ''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, who is currently captain of the England under-19 side, made his Premier League debut on the opening day of last season and went on to appear in 22 league games.
''I am so happy to be signing for Arsenal,'' Chambers said. ''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 teammates today and beginning preparation for the season ahead.''
Southampton indicated it had no choice.
''Calum made it clear to us that he did not see his future at Southampton,'' executive director Les Reed said. ''As such, it was crucial that we were able to negotiate a substantial fee that also reflects the work our staff have put into Calum's development since he joined the club at the age of eight.
''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.''