Last week Championship winners London Welsh won their appeal against a Rugby Football Union decision to block their promotion.
The decision condemned the Falcons, who finished bottom of the top flight, to the drop.
A statement on the north-east club's website read: "Newcastle Falcons confirm there will be no appeal of the decision made by the independent panel to uphold London Welsh's appeal and relegate the Falcons to the Championship.
"We are now looking forward to an exciting new era under the guidance of incoming director of rugby Dean Richards.
"Richards' first league game in charge will be Bristol on the weekend of Saturday September 1 with the first home game of the campaign against Doncaster Knights on Friday September 14."
London Welsh were originally denied the right to go up after being told they had failed to meet the minimum standards required of a Premiership club.
They were initially told they had failed the minimum standards audit on a number of factors but primarily because they did not meet the requirement for primacy of tenure.
In effect, that meant London Welsh were not allowed to share the Kassam Stadium with Oxford United even though three existing Premiership teams co-habit with football clubs.
London Welsh argued the primacy of tenure rule breached UK and European competition law and was therefore void and unenforceable.
The independent panel ruling on the matter agreed.
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