The 30-year-old was part of the Hull squad relegated from the Premier League and was released at the end of last season.
“We are delighted to have brought Liam in as our first summer signing,” Albion boss Chris Hughton said on his club’s official website.
“He’s a terrific professional, has a wealth of experience – which is something that is important for us – and during our negotiations showed a great desire to join us and be part of this club, despite some attractive options elsewhere.”
Rosenior began his career with Bristol City before heading to Fulham and then Reading. He moved to Hull in 2010 and won promotion with the Tigers while also playing in the 2014 FA Cup Final.