The Iranian, 36, finished his commitments with Sweden under-21s - who lost 1-0 to the Republic of Ireland in Dublin on Tuesday night - having verbally agreed a deal to take over at Oakwell.
The former IFK Gothenburg head coach had been on the radar for some time and was interviewed for the position prior to former head coach Gerhard Struber's arrival in November 2019.
He will be assisted by Ferran Sibilia.
Sibilia, 33, was assistant at Gothenburg with Asbaghi and was briefly appointed as caretaker after the Iranian's dismissal last autumn.
Prior to becoming head coach of the Swedish under-21s last November, Asbaghi won the Swedish Cup with Gothenburg in 2020 before being sacked last September.
He has also previously managed Swedish outfits Dalkurd FF and Gefle IF.
Asbaghi's first game in charge will be in Saturday's Championship game at Fulham.
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