The pair, who were also fined, had been suspended for 90 days in October while an investigation was carried out into a 2 million Swiss franc (£1.35 million) payment by FIFA to Platini in 2011. Both men denied any wrongdoing.
The decision, which comes as a corruption scandal swirls around FIFA, means that Blatter's 17 years at the helm of world football will end in disgrace, and spells the end of Platini's hopes of replacing the 79-year-old Swiss in a presidential election in February.
Platini, a former France international who was one of the finest players of his generation and had led the European football body UEFA since 2002, had been the favourite to win that election until he was suspended.
The ethics inquiry began in the wake of the Swiss attorney general's decision to open criminal proceedings against Blatter over the payment to Platini. The office is also investigating the award of the 2018 and 2022 World Cup finals to Russia and Qatar.
In the United States, prosecutors have indicted 27 current or former football officials, including eight former FIFA executive committee members, over allegations that they ran bribery schemes connected to the sale of television rights for football competitions. Twelve people and two sports marketing companies have been convicted.
