Bozovic, 48, was sacked by 1991 European Cup winners Red Star in May following a shock defeat to unfancied Vozdovac that saw them relinquish their lead at the top of the Serbian championship to bitter city foes and eventual champions Partizan Belgrade.
Bozovic has already worked with a number of Russian clubs including Dynamo Moscow, Lokomotiv Moscow and Rostov, with whom he won the Russian Cup in 2014.
Arsenal Tula finished 14th in the 16-team Russian Premier League last season and avoided relegation by winning a playoff against a side from the division below.
Bozovic takes over from former Russia striker Sergei Kiryakov, who left Arsenal Tula last month.
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(Reporting by Vladimir Soldatkin; Editing by Toby Davis)
