The Gunners announced the 28-year-old will "provide competition and support" for Bernd Leno and Runar Alex Runarsson after Matt Macey joined Hibernian in Scotland.
Leno has started all 19 Premier League games for the Gunners so far this season after Emiliano Martinez was allowed to leave for Aston Villa at the start of the campaign.
Runarsson has made four UEFA Europa League appearances and another in the Carabao Cup.
💬 “All those mornings as a young kid in Australia, getting up to watch the Champions League games at four o'clock in the morning when I had school..."— Arsenal (@Arsenal) January 22, 2021
A wholesome first interview ❤️
📺 Introducing... @MatyRyan
Ryan, 28, had been a regular for Brighton, playing 121 Premier League matches in three-and-a-half seasons, but recently lost his place to Spanish goalkeeper Robert Sanchez.
Arsenal boss 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 and look forward to working with him this season."
The keeper, meanwhile, tweeted to say he was "buzzing" to join the club he supported as a child.
Signing for the club you grew up supporting as a kid ✔️ @Arsenal— Maty Ryan (@MatyRyan) January 22, 2021
Buzzing to be beginning this new chapter and will give everything I’ve got to contribute to the first club I ever loved. pic.twitter.com/IUohEjFKVK
Ryan, who has 59 caps for the Socceroos, will wear the number 33 jersey after becoming Arsenal's first signing of the January transfer window.
Technical director Edu added: "Mat is an experienced goalkeeper, a proven talent in the Premier League and has also played many internationals for Australia.
"Mat will further strengthen our squad with his experience and knowledge of playing at the highest level.
"Following Matt Macey’s recent move to Hibernian, Mat will provide very good competition and positive support to all our goalkeepers.
"We are looking forward to him integrating quickly into the set-up here at Arsenal."