The 22-year-old has put pen to paper on a long-term contract and will wear the number six shirt after becoming the club's fourth summer signing.
He follows the permanent additions of Pablo Mari and Cedric Soares after their loan spells and the capture of Willian on a free transfer from Chelsea.
Having beaten a number of Europe's top clubs to his signature, Arteta and technical director Edu gave fans the lowdown on what they can expect from Magalhaes in an Arsenal shirt.
Speaking to the club's official website, Edu said: "We are delighted to have signed Gabriel.
"He is a player we have been studying for a while and he was in demand from many clubs, so we are proud to have agreed and completed this transfer with Lille and the player.
"Gabriel is a player of high quality and Mikel and his coaches are looking forward to integrating him into the club."
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Arteta added: "We welcome Gabriel to Arsenal. He has many qualities which will make us stronger as a defensive unit and as a team.
"He has proved with Lille that he is a defender with many outstanding attributes and we are looking forward to watching him grow as an Arsenal player."
Magalhaes also detailed how Edu and Arteta persuaded him that joining Arsenal was the right move for his career, saying: "[Edu and I] had several chats about Arsenal and the new project, we had many good conversations.
"As the days went by I was getting very excited about it, then I had a call from the coach and that was very reassuring. Having the coach himself calling you to say he wants you in his squad motivates you a lot. That is the very reason I am here today.
"We did not talk about [details], he just told me he is aware of my quality, my capacity and how far I can go. He also said he will be very demanding with me.
"I know he is a great coach and I will make progress with his help."