Hleb, without a club since leaving Turkey's Genclerbirligi, was with Arsenal from 2005-2008 before playing at Barcelona, Birmingham City and several other teams.
BATE have won the domestic title for nine years in a row and lead this season's standings with 38 points from 14 games.
BATE face Partizan Belgrade in the Champions League playoff round, with the first leg on Aug. 19.
(Reporting By Dmitriy Rogovitskiy; editing by Michael Hann)
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