The 28-year-old joined the Gunners from French outfit Dijon in the summer of 2020, earning a £1.7m move to the Emirates thanks to the influence of goalkeeping coach Inaki Cana.
Runarsson arrived to play second fiddle to Bernd Leno after the exit of Emiliano Martinez to Aston Villa, and he made six appearances for the Gunners in the 2020-21 season, including four Europa League starts.
However, Runarsson's only Premier League appearance came as a substitute in a 2-1 loss to Wolverhampton Wanderers, and he has since spent time on loan with OH Leuven, Alanyaspor and Cardiff City.
With Aaron Ramsdale and David Raya battling for the number one jersey, Runarsson is not in Mikel Arteta's plans, and Arsenal have now confirmed that his contract - which was due to expire in the summer - has been terminated.
The Iceland international is now expected to complete a free transfer to Danish champions Copenhagen, who take on Champions League holders Manchester City in the last 16 later this month.
Runarsson was a Super Lig regular for Alanyaspor last season, but he played just eight times for Cardiff in the first half of the 2023-24 campaign.