Why are they banned?
Blatter and Platini were found guilty of ethics code breaches over the "disloyal payment".
Both claimed the payment was honouring an agreement made in 1998 for work carried out between 1998 and 2002 when Platini worked as a technical adviser for Blatter.
The payment was not part of Platini's written contract but the pair insisted it was a verbal agreement, which is legal under Swiss law.
German judge Hans-Joachim Eckert, the chairman of Fifa's adjudicatory chamber, held disciplinary hearings for the pair last week.
Charges included conflict of interest, false accounting and non co-operation, with investigators submitting a file of more than 50 pages.
Statement - key points
The payment made in February 2011 had "no legal basis" in the contract signed by both men when Platini started working for Blatter on 25 August, 1999.
Both men's explanation that there was an "oral agreement" over the payment was rejected as "not convincing".
Blatter's actions did not show "commitment to an ethical attitude", and both men were found to be in "a conflict of interest".
Platini also failed to act with "complete credibility and integrity" and showed "unawareness of the importance of his duties".
The committee said there was "not sufficient evidence" to establish the payment was a bribe, but both men demonstrated an "abusive execution" of their positions.
Blatter - 'I will fight'
Blatter was in defiant mood at a news conference he had called in advance of the punishments being made public.
"I will fight," he said. "I will fight for me and for Fifa."
He said he was "really sorry" that he is still "a punching ball" and that he has become tainted in the eyes of humanity.
He added that he thought he had convinced the Fifa ethics tribunal that the payment from Fifa to Platini was legitimate.
He plans to appeal, first to Fifa, then Cas. He may also take legal action under Swiss law if needed.
Reaction - 'A drowning man'
Fifa reform campaigner Damian Collins and former Football Association chairman David Bernstein believe it is the end for Blatter.
"The fish rots from the head down and we know how rotten the head of Fifa was," said British MP Collins.
Bernstein told BBC Radio 5 Live: "He's a drowning man really, there's no coming back from this.
"He'll fight, I'm sure of that. He's not a soft touch. He will fight but he is doomed. He is yesterday's man."
What will Platini do?
He boycotted his hearing in Zurich on Friday in protest, claiming a decision already appeared to have been made.
His lawyers attended, but it looks as though the Frenchman is preparing to take the matter to Cas.
In the meantime, Uefa has issued a statement, revealing it is "extremely disappointed" with the decision.
It added: "Once again, Uefa supports Michel Platini's right to a due process and the opportunity to clear his name."
What now for Fifa?
World football's governing body has been in turmoil for several months, following numerous allegations of corruption.
Seven Fifa officials were arrested at a Zurich hotel at the end of May.
And US authorities have charged 39 football officials and sports business executives over more than £134m ($200m) in bribes for football television and marketing deals.
Swiss prosecutors are also investigating Fifa's management as well as the award of the 2018 and 2022 World Cups to Russia and Qatar.
