Commander Mike Fincke, Russian Flight Engineer Yury Lonchakov and billionaire Simonyi will be taken by helicopter to the Baikonur space center and then by plane to Russia's space training center, Star City, in the Moscow Region.
Some 12 helicopters, three aircraft and four rescue and evacuation vehicles, as well as a communications vehicle were involved in the search operation in the Kazakhstan steppe.
The Soyuz capsule was originally scheduled to return to Earth on April 7, but the re-entry was postponed after the landing site in Kazakhstan was hit by severe flooding.
Russia's Soyuz TMA-14 spacecraft, carrying two members of the 19th Expedition - Commander Gennady Padalka from Russia and NASA astronaut Michael Barratt - along with Simonyi, docked with the ISS on March 28.
Padalka and Barratt will remain on the ISS for six months, while Japan's Koichi Wakata, who serves as a flight engineer for Expeditions 18, 19 and 20, will return to Earth on board space shuttle Endeavour during its next mission to the orbital station.
NASA has not yet announced the launch date for Endeavour due to delays in previous shuttle missions.
By the end of May, the ISS is due to be constantly manned by six astronauts.