Jose Mourinho has won two Champions League titles as a manager
The Italian club will face Feyenoord in the inaugural final on 25 May in Tirana, Albania.
Mourinho is the first manager to reach the final of a major European competition with four different clubs.
"I am very emotional. This for us is our Champions League," Mourinho said after his side won 2-1 on aggregate.
"When you work in Rome, live in Rome and breathe Rome, you breathe this club because it is the real club of the city.
"I felt from day one it is huge ... but no victories and not many finals. The history is not related to the social dimension of the club.
"We managed to build an OK team that grew step by step so we could beat a Premier League [team]. Of course, I have had bigger moments than this but I am not feeling for myself, I am feeling for the people and my players."
Mourinho guided former clubs Inter Milan and Porto to Champions League titles, before winning the Europa League with Manchester United in 2017.
He joined Roma in May 2021 and it is the first time they have reached a final in European competition since 1991 when they were runners-up in the Uefa Cup.
Serie A reporter James Horncastle told BBC Radio 5 Live: "Mourinho remains a formidable communicator. He said to the fans before, 'Don't just come to the stadium to support us, come to play for us.'
"That's success now. That's what the fans wanted. You saw it in the stands and in the city in the last few weeks. It's given Roma fans something they've been craving for an awful long time."
England striker Tammy Abraham, who scored the winning goal in the second leg at the Stadio Olimpico, added: "Before the game started, the fans won us this game. We could hear them before getting into the stadium and throughout the warm-up.
"The win was for them and my team. Hopefully we can go all the way."
-- Courtesy of BBC Sport