Both were "immediately" banned from all football activity. Blatter, Fifa's president since 1998, was fined 50,000 francs ($50,000).
Platini was fined 80,000 francs.
Blatter and Platini, who had been the most powerful men in football, insisted that the payment made in 2011 had been legitimate following an oral contract.
But Fifa's judges said the "assertion of an oral agreement was determined as not convincing and was rejected by the chamber".
The statement by the court said both showed "abusive execution" of their powers.
Blatter's "actions did not show commitment to an ethical attitude, failing to respect all applicable laws and regulations as well as Fifa's regulatory framework," the court said.
In the case of Platini, the court said he "failed to act with complete credibility and integrity, showing unawareness of the importance of his duties".
For Blatter, 79, the lengthy ban almost certainly marks the end of his career in football administration.
But the unrepentant Swiss said after the ruling that he would appeal the decision.
Blatter said he was "astonished" that judges rejected evidence concerning the existence of an oral contract.
"You ask me if I feel betrayed . . . the answer is yes," the native of the canton of Valais said.
Speaking in English, he added that the ethics committee "deny an evidence and they try to build something up which is not true . . . something that is not true cannot be proven".
He told journalists in Zurich that he had become a "punching ball" at Fifa and that he felt sorry for the scandal-engulfed organization.
"As president of Fifa I am this punching ball," he said.
"I am sorry for Fifa."
Blatter said he would first launch an internal appeal against the suspension at Fifa, before taking his case to the Court of Arbitration for Sport (CAS) in Lausanne.
For Platini, 60, the suspension has derailed his hopes of replacing Blatter at the top of world football's governing body, after having been the favourite to claim the post.
Appeals to an internal Fifa committee and the CAS are possible for both men.