
Arsenal did not disclose the transfer fee but British media reported that they paid £1.5 million for the 25-year-old, who played 13 games in all competitions for Dijon last season.
Runarsson joins the north London club as a back-up to first-choice keeper Bernd Leno following the departure of Emiliano Martinez to Aston Villa.
“We want to create healthy competition for places and we look forward to seeing Alex bring further depth to the goalkeeping position,” manager Mikel Arteta said in a statement.
Runarsson’s signing follows the arrival of Brazilian centreback Gabriel Magalhaes and his compatriot Willian in midfield.