West Ham will face Lyon in the last eight of the Europa League after the draw was conducted in Nyon on Friday.
David Moyes' side made the last eight after an extra-time win over six-time winners Sevilla on Thursday night, with the winning goal coming from Ukraine international Andriy Yarmolenko.
The Hammers could also face La Liga giants Barcelona in the semi-finals if the Catalan side progress from their last eight tie against German side Frankfurt.
Scottish champions Rangers will take on Braga with the first leg in Portugal, while Bundesliga side RB Leipzig are up against Atalanta of Serie A.
Europa League quarter-final draw in full (ties played April 7 and 14)
RB Leipzig vs Atalanta
Eintracht Frankfurt vs Barcelona
West Ham vs Lyon
Braga vs Rangers
Europa League semi-final draw (ties played April 28 and May 5)
RB Leipzig/Atalanta vs Braga/Rangers
West Ham/Lyon vs Eintracht Frankfurt/Barcelona
Meanwhile in the Europa Conference League, Leicester will face a quarter-final tie against Dutch side PSV Eindhoven.
If the Foxes were to win that clash then they'll face the winners of the quarter-final between Norwegian side Bodo/Glimt and Jose Mourinho's Roma.
Hammers boss David Moyes was delighted with his side's historic win over Sevilla after extra-time on Thursday night, but still insisted that his players would be reporting in for duty to training on Friday ahead of the weekend's Premier League clash with Tottenham.
"If you want to be a big club, you have to get used to being in all the time," he said after the match.
"We are climbing a mountain but we are base camp at the moment.
"This result will give us a lot of confidence. We have had two really tough and close games against the side that is second in La Liga.
"People say Spanish football not quite the same but we have seen what Atletico Madrid and Villarreal have done this week [knocking Manchester United and Juventus out of the Champions League ]. Sevilla are above those two.
"This win felt fantastic but we don't get a cup for that. We have to refocus and have another go."
Goalscorer Tomas Soucek added: "I am so happy we can write history at the club. I hope we can do more than today.
"I know when we beat Sevilla we can beat any team."
Rangers made it through to the last eight after they impressively saw off Crvena Zvezda (aka Red Star Belgrade) 4-2 on aggregate, while Barcelona, who dropped into the Europa League from the Champions League, edged past Turkish side Galatasaray over the two matches.
