1057 GMT July 02, 2020
The event's future was thrown in doubt when Sweden withdrew as the host, BBC Sport reported.
But the Russian city of Kazan will stage the games early in 2022.
Special Olympics chairman Tim Shriver admits the decision may be criticized given Russia is serving a four-year ban from all major sporting events.
The Special Olympics is for competitors with intellectual disabilities; there is a focus on participation and personal development rather than medals. The winter games involve some 2,000 competitors from more than 100 countries.
Russia is currently appealing against the sanctions imposed last December by the World Anti-Doping Agency (WADA). Russia's Anti-Doping Agency (RUSADA) was declared noncompliant for manipulating laboratory data handed over to investigators in January 2019.
But the Special Olympics is not a signatory to the WADA code, so even if the ban on hosting major sport is upheld, its winter games can go to Russia.
"We heard this, 'you shouldn't go to Russia'," Shriver told BBC Sport. "Wrong.
"Every time the Special Olympics movement hears you shouldn't include someone, we bristle and we charge and we move forward. We go to Russia in the face of some resistance but with an even greater determination to prove that our athletes can be bridge-builders."
Shriver added, "In almost 52 years, the Special Olympics movement has never had a doping scandal. It's not in our history. We don't play by those rules.
"Why would anyone dope in the Special Olympics movement? We're not interested in whether you're the greatest of all time – we're only interested in what is your greatest performance.
"Russia is not banned from that kind of sport, nor is any other country on Earth, nor is any person.
"So, while the world of sport might be judging by the WADA criteria – which are important, don't get me wrong – we judge by different criteria.
"Are you willing to welcome our athletes, to listen to their voices and their challenge to change the world? Russia has said 'we're ready' and therefore we're ready to go."