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They were found guilty of breaches surrounding a £1.3m ($2m) "disloyal payment" made to Platini in 2011.
The Fifa ethics committee found Blatter and Platini had demonstrated an "abusive execution" of their positions.
"I will fight for me and for Fifa," Blatter, 79, said at a news conference.
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Platini said the decision was a "masquerade" intended to "dirty" his name.
Both men continue to deny wrongdoing and intend to appeal to the Court of Arbitration for Sport (Cas).
Swiss Blatter and 60-year-old Frenchman Platini have also been fined £33,700 ($50,000) and £54,000 ($80,000) respectively.
Despite the ban, both Blatter and Platini will be allowed to attend matches - including Euro 2016 in France - if they buy tickets in a private capacity.
Fifa boss since 1998, Blatter had already announced he was quitting with a presidential election in February.
Platini was tipped as a future leader of football's world governing body and is a three-time European Footballer of the Year.
He is also a former captain of France and has been in charge of Uefa - European football's governing body - since 2007.
Unshaven and sporting a plaster over his right cheek, 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.
Blatter: Key quotes from hour-long news conference
"The decision is no surprise to me," he said in a statement. "The procedure initiated against me by Fifa's ethics committee is a pure masquerade.
"It has been rigged to tarnish my name by bodies I know well and who for me are bereft of all credibility or legitimacy."
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."
Former Asian Football Confederation general secretary Peter Velappan added: "This is very harsh, especially for Blatter because he dedicated his life to football and Fifa. Eight years is like a death sentence."
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Isha Johansen, the president of Sierra Leone's Football Association, said: "I'm not saying Blatter was a saint, but the way everything has been piled on his head to make it look like it was all his fault... I think it's most unfair."
French Football Federation president Noel Le Graet added: "Michel Platini's suspension is shocking and saddens me. It seems unbelievable.
"But it does not surprise me as the ethics commission president had already announced that Michel would be suspended for several years. Michel's guilt was decided in advance."
Football Association chairman Greg Dyke and Fifa reform campaigner Damian Collins believe it is the end for Blatter and Platini.
Dyke told BBC Radio 5 live he had "no sympathy" for Blatter but that the FA "didn't know about Platini" and "were clearly disappointed".
"We thought he had done a very good job as president of Uefa," he added.
British MP Collins said: "The fish rots from the head down and we know how rotten the head of Fifa was."
Former FA chairman David Bernstein told BBC Radio 5 live Blatter was "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."
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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.
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.
There is also pressure from governments and the International Olympic Committee for Fifa to push through major reforms aiming at making governance more transparent and accountable.
The presidential election is due to take place on 26 February.
There are currently five candidates to take over:
Voting will take place by secret ballot, with all Fifa's 209 member states having a vote each.
BBC Radio 5 live sports news correspondent Richard Conway: "You've got this Shakespearean drama between Platini and Blatter - two men who were once the best of friends but have become the best of enemies.
"They have now effectively destroyed each other and their chances. Platini was at one point the favourite to become Fifa president but those hopes lie in tatters.
"Fifa wants to move on and try to re-establish its reputation, it's going to be difficult do that with Blatter and Platini continuing to make noise in the background."
Joseph 'Sepp' Blatter was born in the alpine town of Visp in 1936. Blatter has been married three times and has one daughter.
After finishing school, he did his obligatory service in the Swiss army, rising to the rank of colonel.
He did not play football professionally but worked in the watch industry, then as a sports writer and in sports management, serving at the Swiss Ice Hockey Federation.
Blatter moved to Fifa as its technical director in 1975, before working as the general secretary from 1981.
He was elected, to much fanfare in his homeland, as the eighth Fifa president in 1998, succeeding Dr Joao Havelange.
He has split opinion with his sometimes controversial statements about the game but remains hugely popular with countries in Asia and Africa.
In 2004, he said female footballers should wear skimpier kits to increase the game's popularity and, following the decision to award the 2022 World Cup to Qatar, said gay fans going to the Gulf state, where homosexuality is illegal, should "refrain from sexual activity".
Platini has been boss of European football's governing body since 2007 but rose to fame as one of France's greatest footballers.
The son of a former professional player, he played for Nancy and St Etienne before joining Italian giants Juventus, with whom he was named European Footballer of the Year on three occasions.
A midfielder, Platini also made 72 appearances for France, captaining them to victory at the 1984 European Championship and helping them reach the semi-finals of two World Cups, in 1982 and 1986.
He retired as player at 32, turning to coaching and managed the French national team with mixed results from 1988 to 1992.
After turning down an offer to coach Spanish giants Real Madrid, he was asked by French president Francois Mitterrand to organise the 1998 World Cup in France and, shortly after, was appointed vice-president of the French Football Federation.
Since 2002, Platini has been a member of the executive committee of Fifa and was elected president of Uefa in 2007. He was re-elected and also became Fifa vice-president.
Platini, married with two children, worked as Blatter's technical adviser between 1998 and 2002, but later fell out with his former boss.
Fifa president Sepp Blatter and Uefa boss Michel Platini have been suspended for eight years from all football-related activities following an ethics investigation.