The UK accused the GRU of targeting the "organisers, logistics services, and sponsors" of the games. The 2020 competition was scheduled to take place in Tokyo in July but was postponed due to the pandemic.
UK Foreign Secretary Dominic Raab condemned the GRU's actions in the "strongest possible terms," calling the unit "cynical and reckless," in a statement published on Monday.
The statement also accused the Russian body of targeting the 2018 Winter Olympic and Paralympic Games in South Korea with cyberattacks.
"The UK is confirming for the first time today the extent of GRU targeting of the 2018 Winter Olympic and Paralympic Games in Pyeongchang, Republic of Korea," the government statement said.
"The GRU's cyber unit attempted to disguise itself as North Korean and Chinese hackers when it targeted the opening ceremony of the 2018 Winter Games."
The UK's National Cyber Security Centre has assessed the attacks and believes they were intended to sabotage the games, as the malware used "was designed to wipe data from and disable computers and networks."
The UK statement supplemented major charges announced in the US on Monday.
Six Russian military officers were charged by the US Justice Department, in what was described by officials as a hacking scheme to attack several major foreign powers and former Soviet republics.
The alleged cyberattackers are also GRU members, who stand accused of conducting cyberattacks against the 2018 Winter Games.
US government officials said the officers had hacked into software using destructive malware that blacked out thousands of computers and caused nearly $1 billion in losses.
The attacks were intended to support Russian government efforts to undermine, retaliate against, or otherwise destabilize worldwide computer networks, the US Justice Department said.
The Olympic Games are a popular target for cybercriminals.
In 2016 Russian hackers broke into a World-Anti Doping Agency database through an account created by the International Olympic Committee (IOC) for the Summer Games in Rio. The group stole information about star American athletes like Simone Biles and Venus Williams.
In response to the widening range of threats the IOC and host countries have ramped up cybersecurity efforts in recent years.
In a statement Tuesday, the Tokyo 2020 organizing committee said it "sees cyber security as an important aspect of hosting the Games."
"Although we are not able to disclose details of the countermeasures due to the nature of the topic, we will continue to work closely with the relevant organizations and authorities to ensure that they are thoroughly implemented," it added.
Japan's Chief Cabinet Secretary Katsunobu Kato said that Tokyo was in close cooperation with the US and UK on this issue and would not "overlook malicious cyber attacks that could shake the foundations of democracy."