Former Chelsea striker Tammy Abraham has scored 15 Serie A goals for Roma this season
Tammy Abraham's powerful header for the home side was the difference as Leicester struggled to make an impact at the Stadio Olimpico.
The England striker's goal was enough to prevent the Foxes reaching a first European final after the first leg finished 1-1 at the King Power Stadium.
It will be the Italian side's first European final since 1991, where they will face Feyenoord, who drew 0-0 with Marseille for a 3-2 aggregate win.
Leicester boss Brendan Rodgers said after Sunday's Premier League 3-1 defeat to Tottenham that his side needed to work on their defending of corners - so the last thing he would want to see his side do was concede four of them in the opening 10 minutes.
One of those corners gave Abraham opportunity to leap higher than anyone else and put a bullet header past Kasper Schmeichel from a sublime Lorenzo Pellegrini delivery, whose set-pieces were a threat throughout.
Leicester were passive in the first half and did not manage a shot on target as Jamie Vardy looked isolated up front, with Rodgers seeing fit to introduce a strike partner, Kelechi Iheanacho, at half-time.
The Foxes looked brighter in the second period but still failed to create any clear-cut opportunities as Roma were happy to run down the clock.
The only shots of note came towards the final moments of the game as the Leicester players became desperate, shooting from all distances and angles.
James Maddison's weak effort from 20 yards out was straight at Rui Patricio, and Iheanacho's attempt from distance was also picked up with ease by the Portuguese goalkeeper.
Roma boss Jose Mourinho will now aim to put a fifth European title to his name when his side come up against Dutch side Feyenoord, who beat Marseille 3-2 over two legs in their semi-final, in the final on 25 May in Albania.
Despite Rodgers' admission that he did not know what the Europa Conference League was earlier in the season, Leicester's run in the competition has provided a welcome distraction in an otherwise underwhelming season, where they sit 11th in the Premier League and are without a win in their last four games.
"Of course when you lose a second leg of a semi-final it's disappointing. In the first half it wasn't aggressive enough," Rodgers said.
"The players kept going until the very end but we couldn't find that big chance. There wasn't many in the game for both teams."
But as their chance of reaching a first European final is over, and the likelihood of securing any form of European football next season seems slim, this campaign feels a far cry from last season when they won the FA Cup and finished fifth in the league.
"It's been a great journey for us in Europe in the last couple of years. We have a lot of young players that are finding their way and this was a great experience for them. That will provide motivation for them next season," said Rodgers.
"We just missed out so we're disappointed but we need to finish the season strongly now and look to progress in the summer for next season."
Roma would have been happy to come away from Leicester with the scores level and the second leg was a better tactical showing from Mourinho against his former coaching protege Rodgers.
Mourinho is now the first manager to reach the final of a major European competition with four different clubs.
Leicester's next three league games come against the Premier League's bottom three in Everton, Watford and Norwich so Rodgers will hope his side can salvage a bright finish from a flat season.
-- Courtesy of BBC Sport