The Court of Arbitration for Sport was upholding a previous ruling delivered by FIFA in January 2016.
The ban effectively means Calhanoglu, Leverkusen's joint top-scorer, will miss the majority of the season, which finishes with the German Cup final on May 27.
Football's governing body had found the German-born forward guilty of breaking his contract with Trabzonspor when he left the Turkish side for German side Karlsruher in 2013.
As well as the suspension Calhanoglu was ordered to pay Trabzonspor 100,000 euros ($108,000) in compensation.
In its ruling CAS rejected the player's appeal against both the ban, which was suspended pending the outcome of the appeal, and the fine.
CAS announced it had "dismissed Hakan Calhanoglu’s appeal, but partially upheld the appeal of Trabzonspor in ordering that Hakan Calhanoglu pay 100,000 euros to Trabzonspor FC as reduced compensation for breach of contract without just cause."
After a two-year spell with Karlsruher, the attacking midfielder moved to topflight Bundesliga side Hamburg.
In 2014, he was snapped up by Leverkusen, who are placed ninth in the German championship and face Atletico Madrid in the last 16 of the Champions League in three weeks time.
"Of course, we regret this decision, which is not comprehensible to us," said Leverkusen's sports director Rudi Voeller.
"It's a huge blow to Hakan, but it's also a challenge for us.
"Although Bayer Leverkusen had nothing to do with the events of 2011, we are also being heavily penalised.
"Now, in the decisive part of the season, we will be missing a very important player."
The club's CEO Michael Schade said they will reluctantly accept the punishment, but criticised the verdict.
"Next to the player, it also effects a club, which was absolutely not involved in the events at the time," said Schade.
"Unfortunately, we have no choice, but to accept the verdict."