Dahoud has signed a four-year contract to move to the AMEX stadium as a free agent.
The Syrian-born Germany international spent six seasons at the Signal Iduna Park after joining from Borussia Monchengladbach in the summer of 2017.
Dahoud made 141 appearances in total for Dortmund but a shoulder injury restricted him to just 10 games last season.
The 27-year-old will be Brighton's third summer signing after James Milner and Joao Pedro.
Seagulls head coach Roberto De Zerbi told his club’s website: “I’m excited to have Mahmoud in my team.
“I wanted him when I was at Sassuolo and I’m sure he is going to be a top player for us.”
Brighton technical director David Weir said: “We’re delighted to bring Mahmoud to the club, his quality and ability will really add to the options available to Roberto.
“He’s a quality player, he’s got lots of experience playing at a high level in Germany with great experience in Europe too.”
Dahoud has two caps for the German national team.
Brighton will play Europa League football next season following a sixth place finish in the Premier League last term.
