The 26-year-old has signed a four-year deal through to 30 June 2021.
"Alexandru Maxim is a classic number 10," explained Mainz sporting director Rouven Schröder.
"The ball is his friend, he's confident in one-on-one situations, he can create space with his dribbling and is dangerous from set-pieces.
"He's also got a good feel for running the lines. He will only enhance our squad."
Watch: Stuttgart's top 10 goals in 2016/17
Maxim joined Stuttgart from Romanian side Pandurii Targu Jiu in January 2013. He got his first taste of Bundesliga football a month later, and went on to make a further 130 appearances in all competitions for the south-west club.
The former Espanyol youth player registered five goals and seven assists in 25 Bundesliga 2 outings over the course of last season's promotion-winning campaign.
"I had a fantastic time during four-and-a-half intensive years at VfB," Maxim said.
"The club and the city mean a lot to me, they'll always have a place in my heart. The same goes for the fans, who have always got behind me.
"However, the time had come for me to think about furthering my career. I decided to take on a new challenge at a new club, and I'm happy that, together with VfB, we came to this resolution."