The Gunners have been looking for a new goalkeeper to provide competition for Bernd Leno, with Alex Runarsson struggling to perform this season.
They have now swooped for Ryan, who has slipped down the pecking order at Brighton, and he will join until the summer.
Arsenal manager Mikel Arteta said: “We know Mat very well through his performances with Brighton in recent seasons and he brings additional quality to our squad.
“Mat has very good Premier League experience and has played over 100 times in the league, which is something that will benefit us greatly on and off the pitch. We welcome Mat to Arsenal.”
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