The 2023 Fifa Club World Cup was one of many recent sporting events held in Saudi Arabia
The deal is in place until 2027, giving Aramco sponsorship rights for the men's World Cup in 2026 and the Women's World Cup the following year.
The company already has sponsorship deals within Formula 1 and is a partner of the International Cricket Council.
"Aramco has a strong track record of supporting world-class events, but also a focus on developing grassroots sport initiatives," said Fifa president Gianni Infantino.
The partnership means the Gulf kingdom continues to increase its influence on sport globally.
Saudi Arabia has been accused by critics of investing in sport and using high-profile events to improve its international reputation - a process that has been labelled 'sportswashing'.
It has been criticised for its human rights violations, the 2018 murder of journalist Jamal Khashoggi, women's rights abuses, the criminalisation of homosexuality, the restriction of free speech and the war in Yemen.
A report published in November 2023 found that there were 312 sponsorship deals from Saudi Arabia across 21 sports.
It is the only bidder for the 2034 World Cup, officially launching its campaign in March after Australia pulled out of the running in October. Fifa will confirm the hosts later this year.
Amnesty International said the Aramco deal "raises human rights concerns" and called on Fifa to make "binding agreements with Saudi Arabia to protect people from exploitation, discrimination, and repression" before awarding it the tournament.
The sponsorship deal with Aramco - the biggest oil producer in the world - raises further questions about world governing body Fifa's climate impact.
The 2030 World Cup has drawn criticism from environmental groups because it is being held across six countries from three different continents, but Fifa said it would "take all required measures to mitigate the environmental impact".
In June 2023, a Swiss regulator said Fifa made false claims about the reduced environmental impact of the 2022 World Cup, which was held in Qatar.
Following news of the Fifa deal on Thursday, campaign group Fossil Free Football said: "Saudi Aramco and the Saudi state are determined to keep the world addicted to fossil fuels.
"They now get the world's biggest platform to sell their polluting products and try to clean up their image."
It said Fifa "should break its ties to big polluters", adding: "Fans and players deserve better."
A spokesperson for Greenpeace described it as an "own goal" for Fifa and a "brazen example of sportswashing".
"Aramco is using a sport loved by billions of people around the world to distract the public from the consequences of their climate-wrecking business," the statement added.
"No longer welcome as sponsors by many museums and cultural institutions, oil giants are now all over the world of sport looking for popular brands with which to greenwash their image. Fifa should have shown Aramco a red card instead of rolling out the red carpet."
Independent think tank Carbon Tracker says Aramco is "the world's largest corporate greenhouse gas emitter".
But Aramco says it has "one of the lowest upstream carbon footprints in the industry".
-- Courtesy of BBC Sport