They extended the lease (rather controversially on Ukraine's side) in April 2010, up to 2042.This is from Wiki... I don't know if all of this correct but I do believe Sevastopol was leased by Russia (not owned).
"In 1997, Russia and Ukraine signed the Partition Treaty, establishing two independent national fleets and dividing armaments and bases between them.[9] Ukraine also agreed to lease major parts of its new bases in Sevastopol to the Russian Black Sea Fleet until 2017. During the presidency of Victor Yushchenko (January 2005 – February 2010) the Ukrainian government declared that the lease would not be extended and that the fleet would have to leave Sevastopol by 2017.[10]"
Update: Ukraine, Russia ratify Black Sea naval lease - Apr. 27, 2010
As protesters threw eggs and set off smoke bombs, Ukraine's parliament on Tuesday extended the Russian Black Se… - Apr. 27, 2010. By Interns
archive.kyivpost.com