Stevens departed Rangers earlier this summer after the club chose not to offer him a new contract, despite interest from several top clubs, including Arsenal.
During the second half of last season, Stevens spent time on loan at Scottish Championship side Dunfermline Athletic, making 10 appearances and gaining valuable experience that he hopes to bring to his new team.
In a statement to the club, Stevens expressed his excitement about joining Arsenal, saying, "I'm grateful for the opportunity to be here. I've learned a lot during my time on loan at Dunfermline, and I'm looking forward to showing what I can do at Arsenal."
Arsenal's Academy Manager, Per Mertesacker, also commented on Stevens' move, saying, "Since Archie has been with us, he has impressed as a person and player. He has fit into our environment seamlessly and has been impressive in matches and in training."
Mertesacker added, "We welcome Archie to our Academy and are looking forward to working with him in his continued development."