Chambers become the fifth player to leave the Saints this summer, alongside Luke Shaw, Adam Lallana, Rickie Lambert and Dejan Lovren, and Wenger says he is delighted the Englishman has opted to make the move to north London.
"We are very pleased that Calum has agreed to join us," he told the club's official website.
"The way he adapted to the Premier League last season with Southampton at a young age shows that he has tremendous quality.
"He has a lot of the attributes that we look for in a young player and I am sure that he will do well with us."
Chambers, a Southampton academy graduate, follows in the footsteps of Theo Walcott and Alex Oxlade-Chamberlain in making the move from the south coast to north London.
The 19-year-old could be joined at Arsenal by former team-mate Morgan Schneiderlin, with the Gunners hoping to beat off competition from Tottenham to sign the France international.