Vlaar arrives from Feyenoord for an undisclosed fee believed to be £3.2 million after signing a three-year deal which makes him the fourth acquisition under new manager Paul Lambert.
The move reunites the 27-year-old with former Feyenoord team-mate Karim El Ahmadi, and he also joins Matt Lowton and Brett Holman as a new face at the Birmingham club. Villa have also given Guzan a new three-year contract after the American goalkeeper was briefly a free agent when his former deal at the club was allowed to expire.
Earlier on Wednesday another centre-back, James Collins, left Villa to return to former club West Ham, and the Vlaar deal was completed soon afterwards.
"I am looking forward to following in the footsteps of players such as Paul McGrath, Olof Mellberg and Martin Laursen, of course - all of them great players for this club," Vlaar told the club's official website.
"I know some of Villa's history and I have been in the stadium already and saw all of the pictures of great achievements - it's great. I really believe we can bring the happiness back.
"The stadium is fantastic. I've only seen it so far when there were only a few people around, so I know it will be terrific when it is full of Villa supporters."
Vlaar has nine senior caps for the Dutch national team. He was named in Bert van Maarwijk's squad for Euro 2012 and made two appearances as they exited the tournament at the group stage earlier this summer.