Manchester City get Champions League plum draw
Scottish champions Celtic will meet Israeli side Hapoel Beer Sheva while Irish champions Dundalk have been drawn against Poland's Legia Warsaw.
Celtic beat Kazakh side FC Astana in the third qualifying round, while Dundalk were 3-1 aggregate victors over Belarusian side Bate Borisov.
The two-legged play-off ties will be held on the 16/17 and 23/24 August.
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New City boss Pep Guardiola has won the Champions League twice as a manager - with Barcelona in 2009 and 2011.
The Spaniard has lost in the semi-finals of the competition in each of the past four seasons, once with Barca and three times with Bayern Munich.
City are looking to compete in the group stages of the competition for the sixth successive season.
Steaua, who won the European Cup in 1986 and were runners-up in 1989, finished second to Astra Giurgiu in the Romanian top flight.
City sporting director Txiki Begiristain said: "It's going to be a difficult tie because Steaua are on the up again in Europe and have a lot of talent."
Elsewhere, 2004 winners Porto face a tough tie against Italian side Roma, and 1995 winners Ajax will play Russian side Rostov.
The winners of the ties will progress to the Champions League group stage while the losers will drop into the Europa League.
Ludogorets Razgrad (Bulgaria) v FC Viktoria Plzen (Czech Republic)
Celtic (Scotland) v Hapoel Beer-Sheva (Israel)
FC Copenhagen (Denmark) v Apoel Nicosia (Cyprus)
Dundalk (Republic of Ireland) v Legia Warsaw (Poland)
Dinamo Zagreb (Croatia) v FC Salzburg (Austria)
Steaua Bucharest (Romania) v Manchester City (England)
FC Porto (Portugal) v Roma (Italy)
Ajax (Netherlands) v Rostov (Russia)
Young Boys (Switzerland) v Borussia Monchengladbach (Germany)
Villarreal (Spain) v Monaco (France)