Chelsea will take on Russian side Rubin Kazan, Tottenham tackle Swiss outfit Basel and Newcastle will face Portugal's Benfica.
Rubin Kazan are currently sixth in the Russian Premier League and required extra-time on Thursday to defeat Spain's Levante 2-0 on aggregate in the last 16.
However they are likely to prove tough opponents for Chelsea after knocking out holders Atletico Madrid in the last 32 and emerging unbeaten from a tough group that included Inter Milan.
Rubin's game against Levante was played at Moscow's Luzhniki Stadium - due to problems with their own pitch in the republic of Tatarstan - and they could also face the Blues at a venue where they lost the 2008 UEFA Champions League final to Manchester United.
Swiss champions Basel defeated Zenit St Petersburg 2-1 on aggregate to reach the last eight after hanging on to lose the second leg only 1-0 after the Russians missed a late penalty.
Basel failed to reach the Champions League group stage this season after losing to CFR Cluj in the play-off round.
Benfica, who are currently two points clear in the Primeira Liga, dropped into the Europa League after finishing third behind Barcelona and Celtic in Champions League Group G.
They beat Bordeaux 4-2 on aggregate in the last 16 after scoring two late goals to win the second leg 3-2.
"It's a great draw for us," said Newcastle manager Alan Pardew. "The Estadio da Luz is a great venue. I've been there and it's a fantastic stadium. Importantly, we are at home in the second leg and that will give us an advantage."
Benfica director Rui Costa said: "Newcastle deserve all our respect but we trust in ourselves. We will give it our best to go through."
Europa League draw:
Chelsea v Rubin Kazan
Tottenham v Basel
Fenerbahce v Lazio
Benfica v Newcastle
First-leg ties to be played on April 4, second-leg ties to be played on April 11.
Former Newcastle and Holland striker Patrick Kluivert, who carried out the draw for UEFA, said he believed an English side has a great chance of winning the competition.
The Dutchman said: "There are three great teams from England, Chelsea, Tottenham and Newcastle and for sure one of those can lift the trophy but there will be other teams eager to do so too so that can only be good for the competition."