Beard's resignation has been accepted by the QPR Board of Directors.
Speaking to the club's website, Chairman Tony Fernandes said: “I would like to take this opportunity to thank Phil for his contribution to QPR and wish him well for the future.
“In the short term we will continue to liaise with Phil regarding our long-term projects, ensuring a smooth transitional period prior to making a new appointment.
“I have high regard for Phil and he will always be welcome back at Loftus Road in the future.”
Beard added: “The role of the CEO at QPR has changed in the wake of the recent senior management changes, especially on the football side of the club.
“Whilst the changes have been positive, the decision-making process is evolving all the time at the club and I felt now was a sensible time to move on to other opportunities.
“QPR is a wonderful club and I have thoroughly enjoyed working with the directors and incredible management team and staff at QPR.
“Most of all I want to thank the fans. The passion and loyalty of the Rangers supporters is second to none and I will never forget being one of 40,000-plus R’s fans celebrating our Play-Off Final victory at Wembley in May.
“I’ve thoroughly enjoyed my time at QPR and I wish the club all the best for a bright future.”
Meanwhile, Fernandes has revealed that Chris Ramsey will be given the chance to remain as manager of the club for "a very long time".
Ramsey, 52, was appointed boss until the end of the season on Friday.
But Fernandes has now said Ramsey may remain in charge for longer.