Tottenham will be looking to replicate local rivals Arsenal's recent success against Besiktas after being paired with the Turkish side in Group C of the Europa League.
The Gunners edged past Besiktas over two legs in the Champions League play-offs, with Slaven Bilic's side dropping down to become top seeds in the secondary competition where they face a return to North London.
Also on the agenda for Mauricio Pochettino's side are trips to Serbia's Partizan Belgrade and Greek side Asteras.
Everton, coming from pot three at the draw in Monaco, have a tough draw in Group H, where they play a Lille side spearheaded by on-loan Liverpool striker Divock Origi and Bundesliga outfit Wolfsburg as well as a tricky journey to Russia's Krasnodar.
Scottish champions Celtic avoided meeting Legia Warsaw, the side who they controversially beat in Champions League qualifying due to a technicality, and take the second seed in Group D alongside Salzburg, Dinamo Zagreb and Astra Giurgiu.
The draw throws up two familiar fixtures, with Spurs and Celtic both taking on opponents they have met previously.
Tottenham visited Besiktas' Ataturk Stadium in the group phase of the UEFA Cup in 2006, coming away with a 2-0 win courtesy of goals from Hossam Ghaly and Dimitar Berbatov.
Meanwhile the Hoops last faced Dinamo Zagreb in the Champions League second qualifying round in 1998, losing 3-1 on aggregate after scoring the only goal at Parkhead but losing 3-0 on the road.
Hull, who were beaten on away goals in the Europa League play-offs saw their conquerors, KSC Lokeren of Belgium, handed a gruelling travelling schedule with matches against Trabzonspor, Legia Warsaw and Metalist Kharkiv.
Elsewhere in the draw, holders Sevilla take on Feyenoord in Group G, which also includes Standard Liege and Rijeka, while the top two sides in Group A - Villarreal and Borussia Monchengladbach - also promise a mouthwatering battle.
Inter Milan, who will fancy their chances of making waves in the competition, line up in Group F against Dnipro, St Etienne and first-timers Qarabag of Azerbaijan.
Celtic manager Ronny Deila believes now is the time to put aside the disappointment of losing out to Maribor in the Champions League play-offs.
He told UEFA.com: "It's an interesting group. There are good teams but we are going to fight to go through.
"We are disappointed we didn't make the Champions League but we have to close this chapter for this year and remember the feeling we had.
"We have to work really hard, learn from our defeats and use that experience when we hopefully get in that situation again next year.
"We are going to focus on the 50 or so games we have left and we will do everything to win the league, cups and do well in Europe."