Ryan has agreed a five-year contract and replaces David Stockdale, who left the Amex Stadium to join Birmingham earlier this week.
Ryan, who has won 32 caps, is in the Australia squad for the Confederations Cup in Russia starting on Saturday.
He joined Valencia on a six-year deal from Belgian side Club Brugge in 2015, but made only 10 appearances for the Spanish side, spending last season back in Belgium on loan at Genk.
Brighton manager Chris Hughton said on the club website: “I’m delighted that we’ve been able to attract Mathew to the club, and he will certainly be an excellent addition to the squad in time for our first season in the Premier League.
“We’re very much looking forward to working with him for the season ahead. For somebody of Mathew’s age, he has very good experience, having played in the top divisions in Australia, Belgium and Spain.
“He has also competed in European competition and made a number of appearances at international level.”