Career
Tsveiba started his career at Football Club Dinamo Sokhumi before playing regularly for Football Club Dinamo Tbilisi. In 1990 he left for Football Club Dynamo Kyiv, where he was nominated by the Ukraine. He then played briefly in Russia before signing with Gamba Osaka.
He returned to Russia for Football Club Alania Vladikavkaz, where he was nominated by Russia.
Tsveiba left for the Chinese team Shanghai Pudong, before spending his late career with the Russian teams Uralan Elista and Dynamo Moscow. International career
He was a participant at Italia 90 for the Soviet Union, and at Euro 92 for the Commonwealth of Independent States . Tsveiba played for the Ukraine national team against Hungary in the third national match in August 1992.