Hearts and Partick Thistle have failed to overturn their relegations following an arbitration case.
Hearts and Thistle have also lost out on their demands for a combined total of £10million in compensation.
The pair took legal action against the Scottish Professional Football League after being consigned to the drop as a result of the vote by clubs to curtail the season amid the coronavirus pandemic.
A Court of Session hearing resulted in the case being referred to a three-person arbitration panel convened under the Scottish Football Association rules with a private hearing taking place last week.
According to the promoted clubs, the panel conclusion read: "The tribunal appointed in terms of Scottish Football Association Article 99 issued its decision today.
"It unanimously held that the challenges to the Written Resolution of 15 April 2020 failed, and that the SPFL were entitled to pass, and give effect to, the Written Resolution and all that flowed from it.
"Accordingly it refused to grant any of the orders sought by Heart of Midlothian FC and Partick Thistle FC and continued the arbitration for submissions about expenses."
The SPFL welcomed the ruling with chief executive Neil Doncaster describing it as a "clear, comprehensive and unanimous decision".
I am absolutely delighted that our approach has been vindicated throughout, following an intense period of legal scrutiny and review
"I am absolutely delighted that our approach has been vindicated throughout, following an intense period of legal scrutiny and review," he added.
League chairman Murdoch MacLennan added: "The panel heard from many witnesses, including senior figures from across our game and three members of the SPFL executive team. Thousands of pages of evidence were considered.
"I'm therefore very pleased that the tribunal unanimously held that the challenges to the written resolution of 15 April 2020 failed, and that the SPFL were entitled to pass, and give effect to, the written resolution and all that flowed from it."
Dundee United welcomed the "decisive" verdict after being embroiled in the legal action along with Raith and Cove.
United, who will now kick off their Premiership campaign against St Johnstone on Saturday, added: "We are pleased that today's decision by the tribunal brings this matter to a close, not just for us but for the whole of Scottish football."