Afghan President Hamid Karzai will visit Russia this week to discuss relations between the former foes, the foreign ministry in Kabul said on Monday.
Mr Karzai will travel to Russia on January 20 and stay for two days, an Afghan official told AFP, speaking on condition of anonymity.
The foreign ministry said the invitation came from Russian President Dmitry Medvedev.
The Soviet Union invaded Afghanistan in 1979, sparking a US-backed Afghan resistance that cost hundreds of thousands of lives but eventually forced the Soviet Army to withdraw 10 years later.
But relations between Kabul and Moscow have developed since the US-led invasion of Afghanistan in 2001 and the subsequent installation of the Western-backed Mr Karzai as President.
In November, Moscow and Nato struck a deal to boost the flow of Western military supply shipments through Russia to Afghanistan.
There are about 140,000 Nato-led troops in Afghanistan, around two-thirds of which are from the United States, fighting a Taliban insurgency.
Russia and Afghanistan have also vowed to step up their cooperation against drug trafficking in recent months, despite Kabul's displeasure over a joint US-Russian drugs raid on a laboratory in Eastern Afghanistan in October.