The Gunners had been searching for a new goalkeeper after allowing third-choice Matt Macey join Hibernian on loan for the rest of the campaign.
Arsenal lost the services of Emiliano Martinez to Aston Villa at the start of the season after the Argentine departed in a £20m move.
That prompted Arteta to bring in Alex Runarsson from Dijon as an understudy to Bernd Leno, who is the undisputed number one at the Emirates Stadium.
However, Runarsson is yet to convince when given the chance and two mistakes that resulted in a 4-1 defeat to Manchester City in the Carabao Cup last month sent Arsenal into the market for a new shot stopper.
Ryan comes with a wealth of experience, having made 121 Premier League appearances for Brighton since joining from Valencia in the summer of 2017.
Like much of his time at the Amex Stadium, Ryan started this season as Brighton’s first choice between the sticks but has not played for the Seagulls since a 3-0 defeat to Leicester City on December 13 after losing his position to Robert Sanchez.
"We know Mat very well through his performances with Brighton in recent seasons and he brings additional quality to our squad," Arsenal boss Mikel Arteta told the club's website.
"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."
Ryan wrote on Twitter after his move was confirmed: "Signing for the club you grew up supporting as a kid - Arsenal.
"Buzzing to be beginning this new chapter and will give everything I’ve got to contribute to the first club I ever loved."
Ryan has won 59 caps for the Australia national team.
