Lucescu spent 12 years at the helm of Shakhtar Donetsk from 2004, winning eight domestic league titles and six national cups as well as the UEFA Cup in 2009 to become their most successful coach.
He left the Ukrainian club to join Zenit St Petersburg in Russia, but was dismissed in May after a solitary season in charge.
He has previously coached the Romanian national team, Inter Milan and Turkish clubs Galatasaray and Besiktas.
Terim left his job two weeks after being involved in a brawl in a west coast holiday town.
The 63-year-old former Fiorentina, AC Milan and Galatasaray manager was seen in television footage fighting with a restaurant owner. Turkish media said he and his sons-in-law left five men injured after the incident.