The 73-year-old former Chelsea chairman sealed the deal at 0227 GMT on Friday, and has bought a 50% stake in the club.
Peter Lorimer has agreed to continue in his role as Director and point of contact for the supporters and Peter McCormick will be acting as a consultant to the incoming board but the majority of the current board will step down.
The outgoing Directors agreed to leave their loans of over £4m in the company for the next four years.
The Geneva based Fund is represented by Ken Bates and he said on the official Leeds web-site: "I am delighted to be stepping up to the mantel at such a fantastic club. I recognise that Leeds United is a great club that has fallen on hard times. We have a lot of hard work ahead of us to get the club back to where it belongs in the Premiership and with the helps of the fans, who have stuck by the club through thick and thin, we are going to do everything in our power to ensure that happens.
"Our first task will be to put short, medium and long term plans in place to secure the financial future of the club and these will include buying back, in due course, Elland Road and Thorp Arch. We will also be looking at ways in which the fans can control the football pitch itself. Fans could then ensure that no would be property developer will be able to end the playing of football at Elland Road.
"I wish to pay tribute to the outgoing board. They have done a magnificent job at a time with nobody else would touch Leeds United. It gives me great confidence to know that the outgoing board will remain in close contact and provide all the help needed to ensure a smooth transition in the months ahead.
"I also wish to pay tribute to Trevor Birch for his contributions."
A new Board will be announced at a press conference in due course but it is understood that Lorimer will be joined by former Chelsea finance director Yvonne Todd and Bates' lawyer Mark Taylor.