Drogba struck in each half at the Stade Velodrome to settle the semi-final after a goalless first leg. Marseille will meet Valencia in the final in Gothenburg on May 19.
Ivory Coast forward Drogba, the Ligue 1 player of the year, showed fine individual skill to turn inside defender Aaron Hughes to net after 18 minutes.
His powerful strike from a well rehearsed free kick sealed the win eight minutes from time. He was only denied a hat-trick in the closing moments by a fine Shay Given save and was then substituted to rapturous applause.
Drogba has now scored 11 goals in Europe this season -- his first with the former European champions since joining from En Avant Guingamp. He hit five in the Champions League, which Marseille exited after the first group stage, and he has been on the mark in every round of the UEFA Cup.
Marseille are the second French side to reach a European final in 24 hours after Monaco's Champions League semi-final victory over Chelsea on Wednesday.
Injury-hit Newcastle, without several key players including Wales striker Craig Bellamy and England midfielders Kieron Dyer and Jermaine Jenas and defender Jonathan Woodgate, rarely threatened to deny Marseille their first European final since 1999 when they lost to Parma in this competition.
A cautious opening produced no noteworthy chances, with Given easily dealing with weak efforts from Manuel Dos
CLASSY FINISH
But the Ivorian then demonstrated why he is the hottest property in French football with a classy finish to net the opening goal.
A Newcastle free kick was swiftly cleared out of defence and on a two-against-one break, Camel Meriem released the over-lapping Drogba and his strength and agility allowed him to brush away Hughes and fire home.
The game was halted briefly for a fire cracker to be extinguished behind Fabien Barthez's goal but when it resumed Newcastle were almost caught napping again.
Steve Marlet was afforded too much space down the right but the pacey striker, having evaded the out-rushing Given, was forced wide and the chance went.
The home side put Newcastle under the cosh for the rest of the half, with only a Laurent Robert free kick, skyed over from distance, relieving the pressure for the premier league side.
Newcastle came out with greater purpose after the re-start and Shola Ameobi, using his strength to wriggle free in the area, curled narrowly wide.
Alan Shearer, like his strike partner starved of service in the first half, then forced Barthez to stoop low to save but Marseille's threat on the break was all to evident when Marlet was denied by a deflection.
Newcastle continued to huff and puff without creating a clear-cut chance and their hopes of progressing were extinguished on 82 minutes when Drogba, arriving on the penalty spot, smashed in a free kick rolled into him from the right.