The all-Madrid showdown is a rerun of the 2014 and 2016 finals in Europe's top club competition, with a Cristiano Ronaldo-inspired Real victorious on both occasions in cagey affairs that they failed to settle after 90 minutes each time.
Real -- aiming to become the first team to retain the Champions League — will host Atletico at the Santiago Bernabeu on May 2 and a free-scoring Monaco side brimming with some of Europe's hottest talent are home to Juventus on May 3, with the second legs the following week.
Real Madrid director and former striker Emilio Butragueno said: "We know each other very well, this is the fourth time we meet Atletico in the Champions League but it will not be a final this time.
"Every detail will count and we will have to be very careful, they defend very well and have high-quality players who know how to take advantage of mistakes," he told BeINSports.
Atletico, who boast one of football's most deadly strikers in Antoine Griezmann, will move next season from the Vicente Calderon, their home for 50 years, to a new stadium.
Clemente Villaverde, a former Atletico player and now a director, said the Real clash would be a fitting farewell.
"Our fans and players have experienced two final defeats and know what it means and takes to get there -- a lot of work," he told UEFA.Com.
"Hopefully we can give the Vicente Calderon the goodbye it deserves."
Going into the draw at UEFA headquarters in Nyon, Switzerland all four teams were making the usual noises: there is nothing to choose between any of them, they said publicly.
But the 39-year-old Juventus goalkeeper Gianluigi Buffon broke ranks, saying that he would prefer to avoid a wily Atletico side because they are out of the La Liga title race so can rest players for Europe.
Buffon, one of the best goalkeepers of all time but who has never won the Champions League, got his wish in missing out on Diego Simeone's side, who would dearly love to get one over Real and Ronaldo this time on Europe's biggest stage.
But instead he must face teenage striking sensation Kylian Mbappe, 18, and a rejuvenated Radamel Falcao in a last-four encounter that will be an interesting contrast -- Juventus with their dogged, brilliant defence and a Monaco team that loves scoring goals.
The French side -- Buffon labelled them "feisty" -- are full of attacking vim and have hit a staggering 141 goals in all competitions this season.
Pavel Nedved, the former midfielder who is now an ambassador for Juventus, told BeINSports of the Monaco match- up: "It's 50-50. They have very young players who are under no pressure, who can play without fear.
"That is their strength, their asset."
Vadim Vasilyev, the French side's vice-president, said they would be motivated by the memories of being turfed out of the competition by the Italians in 2015 in the quarter-finals.
"It will be a matter of revenge, clearly," he said. "We're better than two years ago, no doubt about it."
Real Madrid, for whom Ronaldo hit a hat-trick as they saw off Bayern Munich in the quarters, are favourites with British bookmakers.
But Juventus were hugely impressive in beating Barcelona 3-0 in the first leg and then holding the Spanish champions to a 0-0 draw at the Camp Nou on Wednesday in a defensive masterclass.
The final is in Cardiff on June 3.
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