The 22-year-old defender has signed a four-year contract following a move from Middlesbrough on Wednesday evening.
"Joe's a really good player, young and hungry to succeed and he's exactly the type of player we want here at the football club," Lambert told the club's official website.
"There's no doubt in my mind that he will thrive in this environment and he fits in exactly with what we are trying to build here.
"He's an exciting signing for the club and I'm really pleased we've been able to take him here."
Bennett has joined Villa for an undisclosed fee.