The 25-year-old, who had been with Reading since leaving Huddersfield in 2014, started all four of Northern Ireland's matches at Euro 2016 in June.
The former Manchester United trainee joins on a three-year deal at Brighton.
"He's a box-to-box midfielder and an excellent passer of the ball," manager Chris Hughton told the club website.
"He has a good grounding, coming from Manchester United, and gives us extra options in midfield and adds further depth to our squad."
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Brighton & Hove Albion have signed Northern Ireland midfielder Oliver Norwood from fellow Championship side Reading for an undisclosed fee.