The midfielder will join Brighton on a four-year contract on July 1st following the expiry of his deal with the Bundesliga giants
Syria-born Dahoud, who was capped twice by Germany in 2020, becomes the Premier League side's third signing of the summer following deals for Joao Pedro and James Milner.
"I'm excited to have Mahmoud in my team," said Brighton boss Roberto De Zerbi.
"I wanted him when I was at Sassuolo and I'm sure he is going to be a top player for us."
Dahoud began his career with Borussia Monchengladbach before moving to Dortmund in 2017.
He went on to make 141 appearances for this season's Bundesliga runners-up, although his game time was restricted after he had surgery on his shoulder last year.
Brighton are in need of midfield reinforcements having already lost Argentine World Cup winner Alexis Mac Allister to Liverpool and are expected to sell in-demand Ecuadorian Moises Caicedo.