GFH executive Salem Patel told BBC Radio Leeds: "In one or two years' time we want this club to be successful on and off the pitch.
"As a city Leeds is thriving but having a successful football club is absolutely vital."
GFH has confirmed that the deal, which is reported to have cost in the region of £52m, was paid in cash and that Leeds, who are currently 12th in the Championship and were knocked out of the League Cup by Chelsea on Wednesday, are debt free.
Patel believes that the game against the reigning European champions underlined the potential at Elland Road.
"I'm sure all of the bars, clubs and hotels were loving the business generated by the match against Chelsea," he said.
"We had 34,000 in the ground that day and that kind of atmosphere is something we are hoping to recreate every week."
He added: "What we want to do is create a successful but sustainable club and I think every fan will be with us.
"English football is one of the most successful exports that England has at the moment. People are watching world over and being part of that is very exciting to us.
"We want to take Leeds back where they belong."
Patel confirmed that Neil Warnock was a big factor in their decision and he will have support during the January transfer window.
Fellow GFH executive David Haigh came onto the board earlier this month and will be joined by colleagues Patel and Hisham Alrayes.
Leeds fans can breath easy in their beds, with new owners prepared to support the manager and help build a team capable of promotion. Warnock has a decent track record with QPR and Sheffield United of getting unfashionable sides into the top flight. Above all, irrespective of what price the new owners paid for their 100% shareholding the club is in effect debt free which is a strong position to be in.