The highly-rated defender has signed a three-year deal with Albion, and will link up with his new team-mates for the week-long trip to Spain.
Born and bred in Milton Keynes he is a natural left-sided player, but can also play on the right side of defence and has played in midfield during his time with his hometown club.
He has made more than 50 senior appearances since making his debut for MK Dons as a 16-year-old in August 2008. He also had a brief spell on loan at Leyton Orient in January 2012.
Albion's head of football operations David Burke commented, "We are delighted that Adam has joined us. 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."