Russia's dollar-denominated RTS index gained 1.2 per cent at 0900 GMT, while the ruble-denominated Micex went up 1.0 per cent.
Some analysts said that Russia's economy is likely to benefit from Trump's victory, as he repeatedly professed his desire to work with Moscow during the presidential campaign, stirring hopes that his term would bring an ease in sanctions over the Ukraine crisis.
Economy Minister Alexei Ulyukayev was quoted by Russian agencies as saying Wednesday that he "would like to rebuild a higher level of trust and cooperation", including economic, but that it was too early to tell if Trump would fulfil those hopes.
Beyond his statements on Russia and Putin which are applauded by many in Moscow, Trump will not want to cause a rift with Congress by overturning existing Russia policies, he added.