The Championship winners were originally denied the right to go up after being told they had failed to meet the minimum standards required of a Premiership club.
London Welsh's appeal was heard on Thursday by an independent panel, who spent all of Friday deliberating over the evidence before finding in favour of the Richmond-based club.
The verdict condemns Newcastle to relegation after they finished bottom of the Premiership.
The RFU will now instigate an urgent review of the minimum standards criteria, or at least what is left of it, following the verdict.
Newcastle have no provision to appeal the decision through rugby channels and would have to pursue any challenge through the courts.
Although the Falcons say their options are open, the tone of their reaction suggests they will accept the decision and rebuild in the Championship.
Newcastle's new director of rugby Dean Richards took Harlequins back into the Premiership and laid the foundations for the success the club are now enjoying under Conor O'Shea.
A club statement said: "The last time the club was in a similar situation in 1996/97 we bounced straight back and won the Allied Dunbar Premiership trophy in 1997/98 and it is our ambition to replicate similar success.
"We do not underestimate the competitiveness and challenges we face in the Championship but under the tutelage of Dean Richards we will have one, and only one goal - to win.
"Dean has been in this situation with Harlequins and he understands what it takes to navigate through the Championship, whilst putting together a team that will be successful with immediate effect on our return to the Aviva Premiership.
"Winning rugby will be a habit at the Falcons and we expect to bring attacking and exciting play for our fans to enjoy. Add some semi-finals, finals and trophies to the mix and it will be a season to remember.
"For all of you who are still wondering what you should do, commit to the Falcons, join the journey now and have the pride in being able to say 'I was there at the new beginning'."
The promotion and relegation saga has dragged on so long that Friday's verdict comes just six days before the fixtures for the new Premiership season are released.
London Welsh have been linked with a move for Gavin Henson and they have signed three players for the new season - Daniel Browne, Ed Williamson and Matt Keyte - but they will need more to make an impact on the top flight.
A club statement described their appeal success as a victory for sport.
In addition to focusing on anti-competition grounds, London Welsh argued that promotion and relegation should be determined on the pitch, so far as is possible.
"The fundamental strength of our case was based not only on overwhelming legal merits, including in particular anti-competition grounds, but also, equally importantly, on the fairness and justice of rewarding through promotion the team winning on the pitch," the club said.
"It is therefore not only a victory for London Welsh, its players, coaching staff and all its supporters but also for sport in general and the game of rugby union in particular, reinforcing the ethos and fundamental sporting ethic that the best team should receive the appropriate rewards.
"This is reflected in the decision of the Appeal Panel, received earlier this evening."
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