Olympiacos will face Fiorentina in this season's Europa Conference League final on 29 May.
Aston Villa fell short of reaching their first continental final since lifting the European Cup in 1982 following a 6-2 aggregate defeat to Olympiacos in the semi-finals.
Olympiacos are now the first Greek team to reach a major European final in even longer, 53 years after Panathinaikos were European Cup runners-up to Ajax in 1971.
Unai Emery's side, almost certain of qualifying for next season's Champions League by virtue of their outstanding Premier League campaign, lost Thursday night's second leg at the impressive Karaiskakis Stadium in the Athenian port of Piraeus. But the damage had already been done when Olympiacos secured a surprise 4-2 victory in the first leg in Birmingham a week earlier.
Villa had trailed 2-0 at home, before goals from Ollie Watkins and Moussa Diaby levelled things up, only for Olympiacos to then score twice more before the first leg was over.
Olympiacos went further ahead on aggregate early in the second leg through Ayoub El Kaabi and, despite considerable Villa pressure thereafter, went on to see it out. The Moroccan striker eventually put the tie even further out of reach with a second of the game towards the end.
Fiorentina had booked their place in the final 24 hours earlier, successfully overcoming the challenge of Club Brugge. The Italian side scored in stoppage time of the first leg at home to take a slender 3-2 aggregate lead to Belgium, with an 85th minute penalty from Lucas Beltran then enough for Fiorentina to equalise at 1-1 in the second leg and avoid extra-time.
It is their second successive appearance in the Europa Conference League final, having lost out to West Ham United 12 months ago. They have a losing record in finals, beaten in the 1957 European Cup final by Real Madrid, the 1962 Cup Winners' Cup final by Atletico Madrid and the 1990 UEFA Cup final by Juventus, but lifting the 1961 Cup Winners' Cup after facing Rangers.
With the final in three weeks' time to be played at the Agia Sophia Stadium, home of AEK Athens, Olympiacos will not have to travel far. Whoever lifts the trophy will also be guaranteed a place in next season's Europa League group stage as an extra incentive.
