The Saints star is understood to have passed a medical with the Gunners and personal terms are thought to have also been settled.
Chambers, 19, has only made 25 appearances for the South Coast club, but he impressed last season after dislodging Nathaniel Clyne to make it into the Mauricio Pochettino’s XI.
Arsenal themselves have already snapped up Mathieu Debuchy from Newcastle to be their new No. 1 right-back, but Arsene Wenger is a long-term fan of the teenage starlet and sees him as a good back-up man.
Chambers looks set to be Southampton’s fourth major sale of the summer, following the exits of Adam Lallana, Luke Shaw and Rickie Lambert.
Dejan Lovren is another player on the verge of leaving to join Liverpool, while Arsenal themselves are keen to thrash out a deal for midfielder Morgan Schneiderlin.
If all the sales go through the Hamsphire side could have around £100m to spend.