Hearts have lost their arbitration proceedings against the Scottish Professional Football League.
A three-person panel found in favour of the SPFL after a hearing in private last week.
The result means the clubs will definitely begin next season in October in the Scottish Championship and League One respectively.
SPFL chairman Murdoch MacLennan said: “No-one should be under any illusion about the rigorous and challenging nature of this process. I would fully expect all those involved to agree that no stone was left unturned, no allegation left unanswered.
“Every aspect of the various arguments put forward by both Heart of Midlothian and Partick Thistle was examined minutely, with full access to all relevant documents, records, emails and telephone logs.
“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.”
Hearts and Thistle had taken the governing body to court after weeks of discussion over league restructuring – a proposal that would have seen no team relegated for the season ahead – failed to gather enough support from the 42 SPFL clubs.
It remains to be seen if they will pursue the matter further but the verdict by the three-person arbitration tribunal is that relegations from the 2019/20 should stand.
There will also be no compensation for either club as the panel found in favour of the Scottish Professional Football League as well as promoted clubs Dundee United, Raith Rovers and Cove Rangers.