The transfer fee is also a new record sale for the Ligue 1 outfit, while Arsenal said the 26-year-old had signed a “long-term contract”.
The player is expected to travel with the tour party to Sydney this weekend and is likely to make his home debut in the Emirates Cup on July 29 or July 30.
“We are very happy to have Alexandre join our group, Arsenal manager Arsène Wenger said.
“He has shown over a number of years that he can score goals and that he is a very efficient finisher. As well, he has very interesting technical qualities and a strong character.
“So he is a guy who is a great addition for us, and someone who will help us challenge at the top level this season.”