The 27-year-old, who made 18 appearances for the Black Cats during the 2017-18 campaign, will provide back-up to first-choice goalkeeper Mathew Ryan at the Amex next term.
"We're delighted to secure the services of Jason, a goalkeeper that brings a wealth of experience, having played almost 300 games at senior level," Brighton boss Chris Hughton told the club's official website.
"Mat Ryan performed exceptionally well for us in the Premier League last season and Jason's arrival will, following Niki Maenpaa's departure, restore the options we have in this position.
"Jason will work with Ben Roberts (goalkeeping coach) and our other goalkeepers and I'm looking forward to welcoming him to the squad when we return for pre-season training."
Steele started his professional career with Middlesbrough, and has also represented Northampton Town and Blackburn Rovers in the English game.