The 29-year-old centre-back has joined on a free transfer after leaving Bundesliga side FSV Mainz 05.
Balogun, a 6ft 3in defender, has signed a two-year deal with the Seagulls. He began his club career at Turkiyemspor Berlin in July 2007, before moving to Hannover and then Werder Bremen.
Brief spells at Fortuna Dusseldorf and SV Darmstadt 98 followed before he joined Mainz in July 2015, where he made 58 appearances and scored once.
Albion manager Chris Hughton said: "I am delighted to welcome Leon to the club. He will add more depth to our defensive options, and I am pleased to get our first piece of business done so early in the summer.
"He is in the peak years of his career and I am sure he will integrate well into the squad.
"He also has valuable experience, having played in the Bundesliga, the Europa League and at international level."
Berlin-born Balogun is eligible to play for Nigeria through his father, and has 14 caps. He missed out on the 2014 World Cup in Brazil after breaking his foot shortly before the tournament, but has been named in their preliminary 30-man squad for Russia 2018 after helping the Super Eagles to qualify.