The outgoing prime minister's trip is planned for next Monday and Tuesday, following an invitation extended to Olmert by Medvedev.
The two leaders are expected to discuss a number of issues, including Russia's arms supply to Syria, Moscow's objection to additional sanctions on Iran and Israel's peace process with the Palestinians.
Sources in the Prime Minister's Office said the meeting had been planned for some time, after several phone conversations between Olmert and Medvedev after the latter took office.
The officials stressed the Russian president was aware of the political situation in Israel and of Olmert's resignation, as well as the attempts to form a new government headed by Foreign Minister Tzipi Livni, but that he insisted on inviting the Israeli prime minister to Moscow nonetheless.
Israel and Russia disagree on a number of issues, including Syrian President Bashar Assad's attempts to purchase advanced arm systems, including the S-300 – a land-air system which may threaten Israel Air Force planes in longer ranges. This system may also threaten Israeli aircraft flying over Lebanon.
Another issue on the agenda is Moscow's objection to a fourth round of sanctions on Iran in response to the Islamic republic's ongoing nuclear plan.
The Russians are also interested in helping advance the Israeli-Palestinian peace talks, although their offer to host the negotiations as part of the Annapolis peace conference was rejected so far.
In light of the expected timetable for the establishment of a new government, this will likely be Olmert's last visit abroad as prime minister.