0102 GMT March 30, 2020
Besik Kudukhov, who won freestyle 60kg silver at London 2012, died in 2013, BBC reported.
He was found to have taken the steroid turinabol when the World Anti-Doping Agency retested samples this year.
An International Olympic Committee (IOC) disciplinary committee said the case has "now terminated its investigation with no action taken".
Indian wrestler Yogeshwar Dutt — who finished third in London — tweeted in August on hearing of the failed test: "If possible he must be allowed to keep the medal. It will keep his family's honor intact. For me humanity is above everything else."
Vice-president of United World Wrestling, Georgy Bryusov said, "The IOC will not deprive Besik Kudukhov of his silver medal".