Real, who host the May 15-17 showpiece event, beat Anadolu Efes Istanbul 76-63 away for a 3-1 win over the Turkish side in the best-of-five quarter-final series and Olympiakos knocked out visitors Barcelona by the same margin after winning 71-68.
Eight-times winners Real will play dark horses Fenerbahce Istanbul for a berth in the final while Olympiakos lock horns with old rivals CSKA Moscow in the other semi.
There were wild celebrations in Athens when Olympiakos forward Georgios Printezis buried a buzzer-beating three-pointer to put the Greek side through in the Peace and Friendship arena.
Printezis, who sank CSKA in the 2012 final with a last-gasp effort to beat the Russians 62-61 in Istanbul, missed all his five shots behind the arc but kept a cool head at crunch time.
Printezis nailed a slam-dunk to overturn a four-point deficit in the closing stages and sent the crowd into raptures at the end after Euroleague all-time leading scorer Juan Carlos Navarro levelled the scores by hitting one of two free-throws.
Olympiakos fans lit about a dozen flares and hundreds of them invaded the court after the buzzer, joyously mobbing the home players and ripping their red-and-white team shirts.
Playmaker Vassilis Spanoulis, whose versatility helped steer Olympiakos to the title in 2012 and 2013 at London’s O2 Arena, led the charge with 17 points and Printezis added 14.
Real, who will be favourites to end a 20-year wait since they last won the title in 1995, recovered from a narrow defeat by Anadolu in Game Three to brush them aside thanks to a strong final quarter which they won 25-14.
The Turkish side had given their fans early hope that they might force a tie-breaker in Madrid after taking a 9-2 lead, but Real regained their composure with solid long-range shooting as they hit 11 three-pointers from 28 attempts.
Real's ex-Portland Trail Blazers guard Rudy Fernandez scored a game-high 17 points, Sergio Llull got 14 and Sergio Rodriguez added 12, underlining Real’s potent backcourt firepower.
(Editing by Ken Ferris)
