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 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."