The deal has been reported in recent days to be worth around £7m, with Guendouzi agreeing a long-term contract with the Gunners.
"We are delighted Matteo is joining us," manager Unai Emery told Arsenal.com.
"He is a talented young player and a lot of clubs were interested in him. He has big potential and gained good first-team experience last season with Lorient. He wants to learn and improve and will be an important part of our first-team squad."
Guendouzi, who is earmarked as a future prospect more than an immediate regular, will wear the number 29 shirt recently vacated when Granit Xhaka switched to his favoured 34.
The 19-year-old is the fifth Arsenal signing of the summer overall after the earlier captures Stephan Lichtsteiner, Bernd Leno, Sokratis Papastathopoulos and the aforementioned Torreira.