The IOC had asked for clarifications regarding the law earlier this month.
"We have today received strong written reassurances from the Russian government that everyone will be welcome at the Games in Sochi regardless of their sexual orientation," IOC President Jacques Rogge said in a statement.
"In his letter Deputy Prime Minister (Dmitry) Kozak underlines that ‘Russia has committed itself to comply strictly with the provisions of the Olympic Charter and its fundamental principles, according to item 6 of which "any form of discrimination with regard to a country or a person on grounds of race, religion, politics, gender or otherwise is incompatible with belonging to the Olympic Movement," said Rogge.
Russia's law caused international outrage and there have also been calls to boycott the Games next year. Several athletes at the world athletics championships in Moscow earlier this month voiced their opposition to the law.
Critics say the new law effectively disallows all gay rights rallies and could be used to prosecute anyone voicing support for homosexuals.
"The Russian Federation guarantees the fulfilment of its obligations before the International Olympic Committee in its entirety," Kozak wrote in his letter to the IOC.
"In particular, legislation of the Russian Federation does not stipulate any restrictions or differentiation of the rights and responsibilities of citizens on the basis of sexual orientation.
"Discrimination against sexual minorities, just as any other discrimination, is expressly forbidden by the Constitution of the Russian Federation."
(Reporting by Karolos Grohmann, editing by Pritha Sarkar)
