Jurgen Klopp’s men will play Real Madrid after a breathless semi-final second leg which they lost 4-2 on the night.
Liverpool’s 5-2 victory over Roma at Anfield on 24 April was enough to secure them a place in their first final since 2007.
Sadio Mane put Liverpool ahead after just nine minutes at the Stadio Olimpico, only for James Milner’s own goal to bring Roma level six minutes later.
Georginio Wijnaldum’s strike gave Liverpool the lead once more after 25 minutes, putting them 7-3 ahead on aggregate.
Roma needed to net four goals to force extra time, and the Italian side piled on the pressure in the second half with Edin Dzeko scoring seven minutes after the break.
An 86th minute strike and a goal from the spot eight minutes later, both from Radja Nainggolan, gave Roma victory on the night but were not enough to secure the tie.
Nainggolan barely celebrated after his first goal, despite it being a superb strike from 25 yards which went in off the far post.
Liverpool will take on holders Real Madrid in the final at Kiev’s Olympic Stadium on 26 May in a repeat of the 1981 decider which the Reds won 1-0.
Defending champions and 12-time winners Real are bidding for their third successive title, while Liverpool are seeking the sixth in their history.
Two Italians were charged with violent disorder and inflicting grievous bodily harm when Liverpool and Roma faced each other for the first leg in Merseyside.
Sean Cox, a 53-year-old Liverpool fan, suffered serious head injuries and was left in a critical condition.
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Liverpool urged its supporters to avoid areas in the north of Rome ahead of the second leg in the Italian capital.
And after the game, Liverpool stars held aloft a flag bearing Mr Cox’s name.