The Pirates have opted against the independent audit required to earn a place in the Premiership in the event of promotion, meaning the winner of the Championship play-off between the two sides will in fact win nothing.
London Welsh won the first leg of the play-off 37-21 in Penzance and are expected to appeal the RFU's decision.
Newcastle, who were ostensibly relegated from the top division on the final day of the season when their 14-10 victory over London Wasps was not enough to overtake their fellow strugglers at the bottom of the league, will now remain in the Premiership for the 2012-13 season.
The RFU said in a statement: "The Rugby Football Union's board of directors has considered the findings of the independent audit report requested by London Welsh, which determines a club's eligibility for promotion to the Aviva Premiership in line with the minimum standards criteria.
"The report, carried out by independent auditors, found that London Welsh has not met the MSC for the Aviva Premiership.
"The independent auditors identified various failures, including not having primacy of tenure at their nominated ground.
"This states that a club must demonstrate that they can host home fixtures at the time stipulated by Premiership Rugby and/or the host broadcaster.
"The RFU board ratified the findings and agreed, should London Welsh win the RFU Championship final following the second leg on May 30, they would not be eligible for promotion and Newcastle Falcons would remain in the Aviva Premiership.
"Cornish Pirates did not choose to have an independent audit of the Mennaye Field and so do not fulfil the criteria for promotion should they win the final.
"As a result, there will be no promotion from the RFU Championship this season."
Welsh have 14 days to appeal and are almost certain to do so.