The 21-year-old, who has been at the Dons since 2008 and made his debut at 16, will stay with the Seagulls until the summer of 2016, having joined for an undisclosed compensation fee.
"We are delighted that Adam has joined us," head of football operations David Burke said. "Our scouting department have been aware of him and impressed with his progress at MK Dons.
"He has all the attributes that we are looking for and already has a good knowledge of our playing style, having come through the ranks at MK Dons.
"He has great potential to establish himself in the Championship, and we are delighted that he has chosen Brighton & Hove Albion."