The 19-year-old, described as a "gamble" by Arsene Wenger, will join the Gunners as competition for Mathieu Debuchy.
The Gunners have been chasing the 19-year-old for the past month and, after agreeing to 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 12 million euros, becomes the latest Southampton academy product to move to 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.
Chambers is expected to provide competition and cover for Mathieu Debuchy, who joined the FA Cup winner from Newcastle earlier this summer, and his arrival could pave the way for Carl Jenkinson to join Hull City.
Wenger has previously hailed Chambers's versatility, being able to play across the back line and in midfield, though he acknowledges the signing does represent a gamble for Arsenal.
"He can play at center back, right back and central midfield," said the French boss. "I hope he will give us competition for the players in these three positions. He hasn't played many games, no, but the English players on the market in England are very expensive and at the end of the day I was ready to take a gamble because he is a player for the future."