The 22-year-old Romania international, who won the first of four caps last year, joins from first-division club Pandurii Targu-Jiu.
"With Alexandru Maxim we have acquired a technically skilled player who can be used in several positions in midfield. We see a lot of potential to develop," said Stuttgart sports director Fredi Bobic.
Stuttgart, in 11th place and still competing in the Europa League, extended coach Bruno Labbadia's deal on Wednesday, and have also brought in Federico Macheda on loan from Manchester United.
They extended contracts with five players during the winter break.
- Sports & Recreation