Delirious fans, long starved of success on the top European stage, honked car horns and waved giant flags in Milan city centre long into the night after the 1-0 semi-final, second leg defeat at holders Barcelona secured 3-2 aggregrate win.
The 1964 and 1965 winners meet Bayern Munich in the final in Madrid on May 22.
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One banner at the airport read "Welcome Back Heroes" after Mourinho had lauded the rearguard action of his 10-man team and said reaching the final was better than winning the trophy in 2004 with Porto.
Defender Ivan Cordoba described the reaction at the airport as "madness" while team mate Maicon was more cautious given the team, chasing an unprecedented treble of Serie A, Italian Cup and Champions League, could still end up losing all three.
"We haven't won anything yet," the Brazilian told reporters.
However, fans said they could be forgiven for the hysteria after a topsy-turvy season where Inter started slowly in Europe and had looked to have thrown a fifth straight scudetto away before rising back to the top in Serie A with three games left.
A cup final with title rivals AS Roma awaits on May 5.
"It is an indescribable emotion, Mourinho is the greatest coach in the world. I've got tears in my eyes," Inter fan Marco told Reuters.
Mourinho, at loggerheads with the Italian media and football establishment for his outspoken views, has always been adored by Inter fans despite saying he hates Italy and one day wants to coach in Spain or even return to former club Chelsea.
His future is uncertain whether success follows or not even if Italian media are hailing his tactical genius, and the grit he instills in his players, after dogged Inter repelled Barca and Chelsea this term amid flashes of their own brilliance.
