The 22-year-old joins from Vojvodina de Novi Sad, who play in the Serbian league, and has already arrived in Seville with a view to undergoing his medical test and probably signing his contract Thursday, reports Xinhua.
Sevilla have already confirmed on their official website that is all goes according to plan, Stevanovic, who has played five times for his country, will be officially presented to the press and supporters of his new club the same day.
He is believed to have cost around $2 million and will be able to line up alongside his fellow countryman, Emir Spahic, who also plays for the football club.
Meanwhile Celta Vigo have also moved in the transfer window to strengthen their squad for what looks like a battle against relegation in the second half of the season.
The side which returned to the top flight at the end of last season, have confirmed a deal to bring Russian born Norwegian international defender Vadim Demidov back to Spain from Eintracht Frankfurt in a loan move until the end of the season.
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Celta become Demidov' s second Spanish club after he spent a slightly disappointing season and a half with Real Sociedad before leaving to join Enitracht on a three year contract last summer.