The Black Cats, who finished seventh in the Premier League last season, share AC Milan as an opponent with Bournemouth, whose own meeting with the Italian giants comes at home.
The Cherries, playing in Europe for the first time in the club's history, will also face Real Sociedad among their eight group games.
Crystal Palace, last season's Conference League winners, were handed arguably the toughest route of the three English Europa League entrants, drawn against Lyon, Real Sociedad and Beşiktaş in what is the club's first-ever Europa League campaign — a step up forced by Palace's demotion from the Conference League last July for breaching multi-club ownership rules.
Elsewhere, Scottish champions Celtic dropped into the Europa League after squandering a four-goal aggregate lead against LASK in their Champions League play-off tie earlier this week, and will now face Marseille, Benfica and Beşiktaş.
In the Conference League, Brighton's draw includes games against Monaco and Spanish side Getafe, while Hearts have also been paired with Monaco as well as a trip to face Mohamed Salah's Trabzonspor.
This season's Europa League final will be staged in Frankfurt on 26 May, with the Conference League final following six days later in Istanbul.
Europa League fixtures in full:
Sunderland: AZ Alkmaar (home), AC Milan (away), GNK Dinamo (home), Anderlecht (away), Jagiellonia (home), Lech Poznań (away), Levski Sofia (home), Torreense (away)
Bournemouth: AC Milan (home), Real Sociedad (away), Viktoria Plzeň (home), Sparta Praha (away), Sturm Graz (home), Celta Vigo (away), Hapoel Be'er Sheva (home), Lillestrøm (away)
Crystal Palace: Real Sociedad (home), Lyon (away), Sparta Praha (home), Salzburg (away), Lech Poznań (home), Jagiellonia (away), Hoffenheim (home), Beşiktaş (away)
Conference League fixtures:
Brighton: Monaco (home), Panathinaikos (away), Craiova (home), Getafe (away), Kauno Žalgiris (home), Jablonec (away)