The matches will be played from Sept. 12-14 on an indoor hard court at the Tere Tennis Centre in Tallinn.
Belgium asked for the tie to be moved out of Ukraine due to the political unrest in the region which has seen pro-Russian armed separatists clash with loyalist supporters.
Further security concerns were raised in July after Malaysia Airlines Flight MH17 was shot down while flying in Ukrainian airspace and crashed on land controlled by pro-Russian separatists.
The incident resulted in the death of all 298 passengers and crew on board.
Belgium need to win to stay in the World Group while Ukraine are attempting to join the elite nations for the first time.
(Reporting by Pritha Sarkar, editing by Tony Jimenez)
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