Newcastle's opponents Benfica came into the Europa League knock-out stages after finishing third in a Champions League group including Celtic and Barcelona, during which they achieved a 0-0 draw at the Nou Camp.
The three English teams remaining in the Europa League were kept apart in the quarter-final draw. Chelsea face a long trip to take on Russian side Rubin Kazan while Newcastle will play Benfica from Portugal.
In the other quarter-final, Fenerbahce from Turkey will play Italian side Lazio.
Rubin Kazan will be tough opponents for Rafa Benitez's Chelsea team. The Russian side have already knocked out two Spanish teams - holders Atletico Madrid in the last 32 and Levante on the eve of the draw.
Rubin were also unbeaten in a tough group that included Inter Milan, and are particularly strong defensively, having conceded only three goals in 10 European matches.
Spurs' opponents Basle scraped into the quarter-finals after Russian side Zenit St Petersburg missed a late penalty.
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.
Kluivert: "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."
Thursday 4th April Quarter Final (First Leg)Thursday 11th April Quarter Final (Second Leg)Thursday 25th April Semi Final (First Leg)Thursday 2nd May Semi Final (Second Leg)Wednesday 15th May The Final
The chance of Real Madrid meeting Barcelona in the Champions League final at Wembley remained alive when the Spanish giants were kept apart in the draw for the quarter-finals. Barcelona will face David Beckham's side Paris St Germain - he is the only English player left in the competition - while Real Madrid will take on Galatasaray.
In the other two quarter-finals, Bayern Munich's reward for seeing off Arsenal is a meeting with Celtic's conquerors Juventus, while Borussia Dortmund will play Spanish side Malaga.
Unlike in previous seasons, UEFA did not also make the draw for the semi-final pairings at the same time - that will now take place next month.
Real Madrid head coach Jose Mourinho is aiming to become the first manager to win the Champions League with three different clubs, having achieved it previously with Porto and Inter Milan.
His side saw off Manchester United in the first knockout round and also qualified from a tough group comprising the domestic league champions of Spain, Germany, England and Holland.
Steve McManaman, the former Liverpool and Real midfielder who carried out the draw for UEFA, said: "Real have had to do it the hard way so far - they have beaten a lot of good teams."
Galatasaray's squad include two former Mourinho favourites - ex-Chelsea striker Didier Drogba and former Inter midfielder Wesley Sneijder.
Barcelona, who came from 2-0 down in the first leg of the last round to beat AC Milan 4-2 on aggregate, will come up against their former striker Zlatan Ibrahimovic.Champions League quarter-finals:Malaga v DortmundReal Madrid v GalatasarayPSG v BarcelonaBayern Munich v Juventus.
Source: Newcastle United Mad