The transfer fee is also a new record sale for the Ligue 1 outfit, worth an initial 53m euros, according to a statement on the Lyon website.
“We are very happy to have Alexandre join our group. He has shown over a number of years that he can score goals and that he is a very efficient finisher,” Arsenal manager Arsene Wenger said.
“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.”
He had been at Lyon since the age of 12, and scored 129 goals for the senior team, including 100 in Ligue 1.
The 26-year-old, who has made 11 international appearances for France, last season became the first player to score 20 goals or more in three successive French top-flight seasons since Jean-Pierre Papin in 1992.
The forward’s arrival is Arsenal’s second signing of the summer so far following the capture of Sead Kolasinac from Schalke.