The Gunners have beaten Liverpool to the signature of the promising 19-year-old right back, who completed a medical with the North London club on Friday
The promising 19-year-old is now expected to be announced as a Gunner early next week after completing a medical with the north London club on Friday.
Arsenal had already agreed a fee with Southampton to sign the defender, which will see Arsene Wenger's side pay an initial €12m for the teenager in a deal which will rise to €20m.
Liverpool was also interested in signing Chambers, but the promising youngster has followed former Southampton youth products Theo Walcott and Alex Oxlade-Chamberlain in linking up with Arsene Wenger.
Chambers will follow Mauricio Pochettino, Rickie Lambert and Adam Lallana out of St Mary's this summer, while Dejan Lovren and Morgan Schneiderlin could also be on the way out.
The Gunners have re-emerged as rivals for Tottenham to sign Schneiderlin, while Liverpool is closing in on Lovren.
Southampton boss Ronald Koeman had hoped to keep Chambers as competition for Nathaniel Clyne, but the Dutchman reluctantly accepted the transfer would go through.
Arsenal boss Wenger, who has also signed Mathieu Debuchy from Newcastle United this summer and seen Bacary Sagna move to Manchester City, is now expected to let Carl Jenkinson leave the Gunners in a loan deal.
Sunderland, Swansea, West Ham and Hull have all shown an interest in the 22-year-old, who has failed to establish himself as a first team regular since moving to Arsenal as a teenager in 2011.