Madrid initially appealed the ruling, which was imposed when the club was banned from all transfer activity during the summer of 2016 and winter transfer window in 2017 for breaking laws relating to signing global players under the age of 16.
Yesterday, the news was streaming out that Man United had made him their top target and would employ the same financial force they used to sign Paul Pogba last summer to secure his friend and worldwide teammate. Atletico had reportedly lined up Lyon forward Alexandre Lacazette as a replacement for Griezmann.
Griezmann last week publicly declared he could join United in the summer transfer window, rating his chances as being six out of ten in an interview.
Atleti had hoped to bring in Diego Costa should Griezmann leave the club, but their ban means they would not be able to sign someone to cover for the Frenchman's potential departure.
The both Madrid based sides were also hit with a £622,000 fine, however, CAS reduced Real's suspension by a year, but decided not to rule in a similar style on Atletico.
The panel cut the fine imposed by Federation Internationale de Football Association on Atletico to 550,000 Swiss francs ($566,000) from 900,000 Swiss francs ($927,000).
Atletico Madrid fans react during the last match at Vicente Calderon as Atletico Madrid bids farewell to its home of 51 years before moving to the newly-built Wanda Metropolitano, in Madrid Spain May 28, 2017.
Atletico have criticised the CAS ruling in a five-point statement on their website, describing it as "unfair" and saying they had been "penalised despite strictly complying with the Spanish legislation". The Turkey midfielder was then sidelined for several months before making his debut in January 2016.