The 19-year-old, who has already completed a medical ahead of his switch to the Emirates Stadium, is expected to become Wenger’s fourth major summer signing for a reported £16million fee.
Wenger has already boosted his squad with the arrivals of Alexis Sanchez, Mathieu Debuchy and David Ospina, but Chambers will provide defensive cover following the departure of Bacary Sagna, while Thomas Vermaelen is also reportedly set for an exit.
The versatile England Under-19s international has made just 22 Premier League appearances for Southampton since his first-team debut in 2012, but Wenger believes he will prove to be a valuable addition.
"He can play at centre-back, right-back and central midfield. I hope he will give us competition for the players in these three positions," Wenger told several national newspapers.
"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."
Meanwhile, Wenger is set to take his squad to Austria for a pre-season training camp but will be without Sanchez, who faces a delay in making his Arsenal debut after joining from Barcelona.
Wenger explained: "I don’t think Sanchez will come to Austria because he has to go to Paris to get a visa.
"So he will only go to London Colney on Tuesday and we come back on Thursday, so he will work in London."
The Gunners will then return to England for the Emirates Cup, where they are set to take on Benfica and Monaco, before heading to Wembley to contest the Community Shield against Manchester City.
However, Wenger has bemoaned how difficult the summer’s World Cup has made it for him as he prepares for the new season.
"The real work starts now and then the Emirates Cup this weekend," he said.
"The problem is our pre-season is very short – these post-World Cup campaigns are a nightmare for us because we have no preparation."