The Croatian will take over after the sacking of former manager Russell Martin earlier this week.
BBC Sport says Juric will sign an 18-month contract with Saints.
He moves to St Mary's after a short spell at AS Roma earlier this season. Juric stepped down as coach of Torino at the end of last season.
Juric's announcement is expected within the next 24 hours.
Southampton had also considered Juric before replacing Ralph Hasenhuttl with Nathan Jones.
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