The promoted side are without a point in six Serie A matches this season and have turned to the 53-year-old, who had been without a job since leaving Cremonese in March.
Venezia are rooted to the foot of the table, four points behind second-bottom Fiorentina, following a 3-1 loss at Atalanta on Monday in Stroppa's final game in charge.
Stroppa was the fourth coach to be sacked in Serie A already this season, after Fiorentina fired Fabio Grosso, Domenico Tedesco left Bologna and Carlos Cuesta was dismissed by Parma.
Nicola's first game in charge of Venezia will be against Napoli on Saturday.
Nicola has developed a reputation for inspiring escape acts in the Italian top flight from previous spells at Crotone, Genoa, Torino, Salernitana and Empoli.