In a deal worth a reported 52 million pounds ($84.6 million), GFH have bought the club from majority shareholder Ken Bates, a familiar figure in the English game who was previously owner of Chelsea.
Bates, 81, is not severing all ties with Leeds. He will remain club chairman until the end of the season.
Agreement was first announced a month ago and the details were finalised on Thursday evening, the club said in a statement on its website (www.leedsunited.com).
The target for Leeds is a return to the lucrative English Premier League for the first time since 2004. Leeds are currently in 12th place in the 24-team Championship (second division).
"We don't really want to put a timescale to our investment, but we hope to be able to make this club as successful as we can in the shortest time possible," said GFH executive David Haigh.
The club last won the English top-flight title in 1992, the final season before the Premier League was launched.
($1 = 0.6150 British pounds) (Writing by Keith Weir, editing by Justin Palmer)