QPR hope to begin work on the Warren Farm sports ground development, after the Supreme Court rejected attempts to overturn planning permission.
Hanwell Community Forum had sought permission to appeal against the planning permission, and whether the council had acted appropriately.
The High Court and Court of Appeal had previously confirmed as such.
This dispute has been a long-running affair, as Rangers had initially hoped to move in for the 2013-14 season.
"We're delighted that all legal avenues to frustrate this process have now been exhausted," QPR chief executive officer Lee Hoos said.
"A new training ground, which brings together the first team and the academy, is an important part of a strategic long-term plan for the club.
"The delays have been very frustrating. Not only have they delayed us securing a new training ground for the club but they have delayed the huge community benefit to residents from improved sports facilities and the programmes that QPR in the Community Trust will run at Warren Farm.
"We look forward to engaging with Ealing residents, sports clubs and the council about those facilities and programmes as construction gets under way."