In a verdict that heightened the crisis in football's scandal-plagued world body, the court strongly criticised the FIFA president and vice president, saying there was "no legal basis" for the payment that Blatter authorised for Platini in 2011.
While full-blown corruption charges were dropped, both men angrily vowed to fight the bans.
Blatter said he felt he was being used as a "punching ball" and declared: "I will fight to the end."
The ban, which starts immediately, promises to end 79-year-old Blatter's four decades with FIFA in disgrace. It is also a devastating blow to Platini's hopes of taking over as head of FIFA in an election on February 26.
The German federation's acting leader Reinhard Rauball said "changing faces" would not be enough for FIFA. "They must regain trust and credibility. It is going to take years."
"I think this is punishment enough, because it means they can never come back," former UEFA president Lennart Johansson told the Swedish daily Expressen.
Blatter, FIFA's president since 1998, was fined 50,000 Swiss francs (USD 50,000/46,300 euros) while Platini, the head of UEFA, Europe's governing body, was fined 80,000 Swiss francs.
A statement by the FIFA tribunal said Blatter and Platini were guilty of "abusive execution" of their powers over the payment.
The judges said there was a conflict of interest and "no legal basis" for the transfer in their written agreement on advisory work by Platini between 1999 and 2002.
Blatter's "assertion of an oral agreement was determined as not convincing and was rejected by the chamber."
The judgement was even more damning of French football legend Platini.
"Mr Platini failed to act with complete credibility and integrity, showing unawareness of the importance of his duties and concomitant obligations and responsibilities.
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