The supporters' trust voted on Monday night to bring their five-year partnership with Bees fan and investor Benham to an end two years early, allowing him to take sole control at Griffin Park.
Benham said: "I am looking forward to the next phase of my involvement with Brentford Football Club now that Bees United members have approved the deal.
"I am very pleased at how the partnership with Bees United has developed, and their role will be as vital as ever as we all strive for greater things for Brentford, which is what we all want to achieve."
Bees United will still have representatives on the club's board and retain a 'golden share'.
BU chairman David Merritt added: "We look forward to continuing to help safeguard the future of the club as we work for future success under Matthew's direct ownership, and as we strive towards our shared aims of a new stadium."