Chambers, 19, continues the exodus of players from St Mary's after agreeing a "long-term" contract with the Gunners.
"Calum has a lot of the attributes that we look for in a young player. I'm sure he will do well with us," Arsenal manager Arsene Wenger told the club's official website.
Chambers, who can also play at centre-back, accumulated 22 appearances for Saints last season after making his Premier League debut on the opening day of the campaign.
"We are very pleased that Calum has agreed to join us," Wenger said.
"The way he adapted to the Premier League last season with Southampton at a young age shows that he has tremendous quality."
The Southampton academy product is the current captain of the England Under-19s and has been moved into defence after starting his career as a midfielder.
"I'm 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 team-mates and beginning preparation for the season ahead.
"I would like to take this opportunity to say thank you to everyone at Southampton for everything they have done for me and for making this move possible."
Chambers' transfer fee is thought to be in the region of £16million and Wenger hopes he will provide competition in midfield and defence.
He will primarily act as right-back cover for France international Mathieu Debuchy, a recent arrival from Newcastle, while Carl Jenkinson is also an alternative in the position.
However, Arsenal are reportedly hoping to send Jenkinson out on a season-long loan with Southampton among his possible destinations.
The arrival of Chambers continues a reasonably busy summer in the transfer window at the Emirates Stadium with Debuchy, David Ospina and Alexis Sanchez having already signed.
It is a different story at St Mary's, however, where a startling player drain means Chambers is the fifth player to depart this summer and he could be followed out the door by Morgan Schneiderlin and Jay Rodriguez.